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<p><a href="index.html">To start page</a></p>
<h3>Publications</h3>
<p>See also my profiles at
[<a href="https://arxiv.org/a/0000-0002-1829-5842.html">arXiv</a>]
[<a href="https://orcid.org/0000-0002-1829-5842">ORCID</a>]
[<a href="https://scholar.google.com/citations?user=kn3azw0AAAAJ">Google Scholar</a>]
[<a href="https://mathscinet.ams.org/mathscinet/author?authorId=311106">MathSciNet</a>]
[<a href="https://zbmath.org/authors/?q=ai:muller.peter.5">zbMATH (Zentralblatt)</a>]
</p>
<ul>
<li>
<strong>Explicitly combing hedgehogs over fields of Stufe 4</strong><br>
[<a href="https://arxiv.org/abs/2605.15452">preprint
(2026)</a>]
</li>
<li>
<strong>A note about Jordan's bound on the size of finite
linear groups</strong><br>
[<a href="https://arxiv.org/abs/2603.15813">preprint
(2026)</a>]
</li>
<li>
<strong>On transitive sets of derangements in primitive
groups</strong><br>
Archiv der Mathematik 126 (2026), 551-556.<br>
[<a href="https://doi.org/10.1007/s00013-026-02240-3">published version (open access)</a>]
[<a href="http://arxiv.org/abs/2304.08459">preprint
(2026)</a>]
</li>
<li>
<strong>On Euler's magic matrices of sizes 3 and
8</strong><br>
Acta Arithmetica 222 (2026), 71-82<br>
[<a href="https://doi.org/10.4064/aa250422-2-8">published
version (open access)</a>] [<a href=
"https://arxiv.org/abs/2504.16260">preprint (2025)</a>]
</li>
<li>
<strong>Transitive sets of derangements in primitive actions
of PSL<sub>2</sub>(q)</strong><br>
[<a href="https://arxiv.org/abs/2512.19500">preprint
(2025)</a>]
</li>
<li>
<strong>Normal subgroups and permutation characters: a
correction to a proof of Klingen</strong><br>
with Pablo Spiga<br>
[<a href="https://arxiv.org/abs/2504.05362">preprint
(2025)</a>]
</li>
<li>
<strong>Another proof of Segre's theorem about
ovals</strong><br>
Advances in Geometry 25 (2025), no. 2, 289-291.<br>
[<a href=
"https://doi.org/10.1515/advgeom-2025-0012">published
version</a>] [<a href=
"https://arxiv.org/abs/1311.3082">preprint (2025)</a>]
[<a href=
"https://mathscinet.ams.org/mathscinet/article?mr=4908009">MR4908009</a>]
[<a href="https://zbmath.org/1570.51006">Zbl 1570.51006</a>]
</li>
<li>
<strong>A note about solvable and non-solvable finite groups
of the same order type</strong><br>
[<a href="http://arxiv.org/abs/2408.07732">preprint
(2024)</a>]
</li>
<li>
<strong>A note on Galois groups of linearized
polynomials</strong><br>
Journal of Number Theory 259 (2024), 238-241.<br>
[<a href=
"https://doi.org/10.1016/j.jnt.2024.01.016">published version
(open access)</a>] [<a href=
"https://arxiv.org/abs/2311.14953">preprint</a>] [<a href=
"https://mathscinet.ams.org/mathscinet/article?mr=4708720">MR4708720</a>]
[<a href="https://zbmath.org/1553.11110">Zbl 1553.11110</a>]
</li>
<li>
<strong>A note on a conjecture by Ulas on polynomial
substitutions</strong><br>
Journal of Number Theory 205 (2019), 122-123.<br>
[<a href=
"https://doi.org/10.1016/j.jnt.2019.06.004">published
version</a>] [<a href=
"https://arxiv.org/abs/1907.13166">preprint</a>] [<a href=
"https://mathscinet.ams.org/mathscinet/search/publdoc.html?pg1=MR&s1=3996346">MR3996346</a>]
[<a href="https://zbmath.org/1436.11031">Zbl 1436.11031</a>]
</li>
<li>
<strong>Decompositions of rational functions over real and
complex numbers and a question about invariant
curves</strong><br>
Illinois Journal of Mathematics 59 (2015), no. 4,
825-838.<br>
[<a href=
"http://www.projecteuclid.org/euclid.ijm/1488186011">published
version (open access)</a>] [<a href=
"https://mathscinet.ams.org/mathscinet/article?mr=3628291"
target="_blank">MR3628291</a>] [<a href=
"https://zbmath.org/?q=an%3A1361.30041">Zbl 1361.30041</a>]
</li>
<li>
<strong>Low-degree planar monomials in characteristic
two</strong><br>
with M. Zieve<br>
J. Algebraic Combinatorics 42 (2015), no. 3, 695-699.<br>
[<a href=
"http://dx.doi.org/10.1007/s10801-015-0597-y">published
version</a>] [<a href=
"http://arxiv.org/abs/1305.6597">preprint</a>] [<a href=
"https://mathscinet.ams.org/mathscinet/article?mr=3403176"
target="_blank">MR3403176</a>] [<a href=
"https://zbmath.org/?q=an%3A1343.51005">Zbl 1343.51005</a>]
</li>
<li>
<strong>On the size of Kakeya sets in finite vector
spaces</strong><br>
with G. Kyureghyan, Qi Wang<br>
Electron. J. Combin. 20 (2013), no. 3.<br>
[<a href=
"http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i3p36/0">published
version</a>] [<a href=
"http://arxiv.org/abs/1302.5591">preprint</a>] [<a href=
"https://mathscinet.ams.org/mathscinet/article?mr=3104534"
target="_blank">MR3104534</a>] [<a href=
"https://zbmath.org/?q=an%3A1295.11138">Zbl 1295.11138</a>]
</li>
<li>
<strong>Permutation groups with a cyclic two-orbits subgroup
and monodromy groups of Laurent polynomials</strong><br>
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. XII (2013),
369-438.<br>
[<a href=
"https://doi.org/10.2422/2036-2145.201012_002">published
version</a>] [<a href=
"http://www.numdam.org/item/ASNSP_2013_5_12_2_369_0/">open
access</a>] [<a href=
"https://mathscinet.ams.org/mathscinet/article?mr=3114008">MR3114008</a>]
[<a href="https://zbmath.org/?q=an%3A1366.20001">Zbl
1366.20001</a>]
</li>
<li>
<strong>Permutation polynomials and translation planes of
even order</strong><br>
with U. Dempwolff<br>
Adv. Geom. <em>13</em> (2013), 293-313.<br>
[<a href="https://doi.org/10.1515/advgeom-2011-050">published
version</a>]
</li>
<li>
<strong>Galois groups of multivariate Tutte
polynomials</strong><br>
with A. Bohn, P. Cameron<br>
J. Alg. Comb. <em>36(2)</em> (2012), 223-230.<br>
[<a href=
"http://dx.doi.org/10.1007/s10801-011-0332-2">published
version</a>] [<a href=
"http://arxiv.org/abs/1006.3869">preprint</a>]
</li>
<li>
<strong>Translation planes of odd order via Dembowski-Ostrom
polynomials</strong><br>
with U. Dempwolff<br>
Osaka J. Math. <em>49</em> (2012), 771-794.<br>
[<a href=
"http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ojm/1350306596">published
version (open access)</a>]
</li>
<li>
<strong>A one-parameter family of polynomials with Galois
group <em>M<sub>24</sub></em> over <em>Q(t)</em></strong><br>
[<a href="http://arxiv.org/abs/1204.1328">preprint
(2012)</a>] [<a href="Papers/m24.sage">accompanying data</a>]
</li>
<li>
<strong>On the non-existence of sharply transitive sets of
permutations in certain finite permutation
groups</strong><br>
with G. Nagy<br>
Adv. Math. Commun. <em>5(2)</em> (2011), 303 - 308.<br>
[<a href="http://dx.doi.org/10.3934/amc.2011.5.303">published
version</a>] [<a href=
"http://arxiv.org/abs/1005.1598">preprint</a>]
</li>
<li>
<strong>A note on the group of projectivities of finite
projective planes</strong><br>
with G. Nagy<br>
Innov. Incidence Geom. <em>6-7</em> (2009), 291-294.<br>
[<a href="https://msp.org/iig/2008/6-1/p18.xhtml">published
version</a>] [<a href="Papers/m24final.pdf">preprint</a>]
</li>
<li>
<strong>Sharply <em>2</em>-transitive sets of permutations
and groups of affine projectivities</strong><br>
with T. Grundhöfer<br>
Beiträge zur Algebra und Geometrie <em>50(1)</em> (2009),
143-154.<br>
[ <a href=
"http://www.emis.de/journals/BAG/vol.50/no.1/9.html">published
version</a>] [<a href="Papers/sharplyTGPM.pdf">preprint</a>]
</li>
<li>
<strong>Factorized spread sets and translation planes with
large homology groups</strong><br>
with U. Dempwolff<br>
Advances in Geometry <em>9(1)</em> (2009), 111-124.<br>
[<a href=
"http://dx.doi.org/10.1515/ADVGEOM.2009.007">published
version</a>]
</li>
<li>
<strong>On Ritt's polynomial decomposition
theorems</strong><br>
with M. Zieve<br>
[<a href="http://arxiv.org/abs/0807.3578">preprint
(2008)</a>]
</li>
<li>
<strong>Quadratic factors of <em>f(X)-g(Y)</em></strong><br>
with M. Kulkarni, B. Sury<br>
Indagationes Mathematicae <em>18</em> (2007), 233-243.<br>
[<a href=
"http://dx.doi.org/10.1016/S0019-3577(07)80019-X">published
version</a>] [<a href="Papers/fxgyintro.pdf">preprint</a>]
</li>
<li>
<strong>Permutation groups of prime degree, a quick proof of
Burnside's theorem</strong><br>
Archiv der Mathematik <em>85,</em> (2005), 15-17.<br>
[<a href=
"http://dx.doi.org/10.1007/s00013-005-1421-z">published
version</a>] [<a href=
"http://arXiv.org/abs/math/0310200">preprint</a>]
</li>
<li>
<strong>The rational function analogue of a question of Schur
and exceptionality of permutation
representations</strong><br>
with R. Guralnick, J. Saxl<br>
Memoirs of the American Mathematical Society, Band
<em>162</em>, AMS (2003).<br>
[<a href=
"http://www.ams.org/bookstore-getitem/item=MEMO-162-773">published
version</a>] [<a href=
"http://arxiv.org/abs/math/0201069">preprint</a>]
</li>
<li>
<strong>Algebraic groups over finite fields, a quick proof of
Lang's theorem</strong><br>
Proc. Amer. Math. Soc. <em>131,</em> 2 (2003), 369-370.<br>
[<a href=
"http://dx.doi.org/10.1090/S0002-9939-02-06591-7">published
version</a>] [<a href="Papers/lang.pdf">preprint</a>]
</li>
<li>
<strong>Finiteness results for Hilbert's irreducibility
theorem</strong><br>
Ann. Inst. Fourier <em>52,</em> 4 (2002), 983-1015.<br>
[<a href="http://dx.doi.org/10.5802/aif.1907">published
version</a>] [<a href=
"http://arxiv.org/abs/math/0109071">preprint</a>]
</li>
<li>
<strong>Arithmetically exceptional functions and elliptic
curves</strong><br>
In: D. Harbater, P. Müller, J. Thompson, H. Völklein (eds),
Aspects of Galois Theory, London Math. Soc. Lecture Notes
256, Cambr. Univ. Press, 1999, 180-201.<br>
[<a href="Papers/ell.pdf">preprint</a>]
</li>
<li>
<strong>Hilbert's irreducibility theorem for prime degree and
general polynomials</strong><br>
Israel J. Math. <em>109</em>, (1999), 319-337.<br>
[<a href="http://dx.doi.org/10.1007/BF02775041">published
version</a>] [<a href="Papers/hit.pdf">preprint</a>]
</li>
<li>
<strong><em>(A<sub>n</sub>,S<sub>n</sub>)</em> realizations
by polynomials - on a question of Fried</strong><br>
Finite Fields Appl. <em>4</em> (1998), 465-468.<br>
[<a href="http://dx.doi.org/10.1006/ffta.1998.0228">published
version</a>] [<a href="Papers/ansn.pdf">preprint</a>]
</li>
<li>
<strong>Exceptional polynomials of affine type</strong><br>
with R. Guralnick<br>
J. Algebra <em>194</em> (1997), 429-454.<br>
[<a href="http://dx.doi.org/10.1006/jabr.1997.7028">published
version</a>] [preprint available upon request]
</li>
<li>
<strong>A Weil-bound free proof of Schur's
conjecture</strong><br>
Finite Fields Appl. <em>3</em> (1997), 25-32.<br>
[<a href="http://dx.doi.org/10.1006/ffta.1996.0170">published
version</a>] [<a href="Papers/schur.pdf">preprint</a>]
</li>
<li>
<strong>An infinite series of Kronecker conjugate
polynomials</strong><br>
Proc. Amer. Math. Soc. <em>125</em> (1997), 1933-1940.<br>
[<a href=
"http://dx.doi.org/10.1090/S0002-9939-97-03892-6">published
version</a>] [preprint available upon request]
</li>
<li>
<strong>Kronecker conjugacy of polynomials</strong><br>
Trans. Amer. Math. Soc. <em>350</em> (1998), 1823-1850.<br>
[<a href=
"http://dx.doi.org/10.1090/S0002-9947-98-02123-0">published
version</a>] [preprint available upon request]
</li>
<li>
<strong>Wan's bound for value sets of
polynomials</strong><br>
with T. Cusick<br>
In: S. Cohen and H. Niederreiter (eds), Finite Fields and
Applications, London Mathematical Society Lecture Note Series
<em>233</em>, 69-72, Cambridge University Press, Cambridge,
1996.<br>
[<a href=
"http://dx.doi.org/10.1017/CBO9780511525988.008">published
version</a>] [preprint available upon request]
</li>
<li>
<strong>Reducibility behavior of polynomials with varying
coefficients</strong><br>
Israel J. Math. <em>94</em> (1996), 59-91.<br>
[<a href="http://dx.doi.org/10.1007/BF02762697">published
version</a>] [preprint available upon request]
</li>
<li>
<strong>On a question of Davenport</strong><br>
with H. Voelklein<br>
J. Number Theory <em>58</em> (1996), 46-54.<br>
[<a href="http://dx.doi.org/10.1006/jnth.1996.0059">published
version</a>] [<a href="Papers/dp.pdf">preprint</a>]
</li>
<li>
<strong>New examples of exceptional polynomials</strong><br>
In: G. L. Mullen and P. J. Shiue (eds), Proceedings Second
International conference on Finite Fields, Contemp. Maths.
<em>168</em>, 245-249, Amer. Math. Soc., 1994.<br>
[<a href="http://dx.doi.org/10.1090/conm/168/01704">published
version</a>] [preprint available upon request]
</li>
<li>
<strong>Primitive monodromy groups of
polynomials</strong><br>
In: M. Fried (ed), Recent developments in the inverse Galois
problem, Contemp. Maths. <em>186</em>, 385-401, Amer. Math.
Soc., 1995.<br>
[<a href="http://dx.doi.org/10.1090/conm/186/02193">published
version</a>] [<a href="Papers/mon.pdf">preprint</a>]
</li>
<li>
<strong>On the collineation group of cyclic
planes</strong><br>
J. Combin. Theory Ser. A, <em>65</em>(1) (1994), 60-66.<br>
[<a href=
"http://dx.doi.org/10.1016/0097-3165(94)90037-X">published
version</a>] [preprint available upon request]
</li>
<li>
<strong>Sharply transitive linear algebraic
groups</strong><br>
Geom. Dedicata <em>45</em>(2) (1993), 203-224.<br>
[<a href="http://dx.doi.org/10.1007/BF01264521">published
version</a>] [preprint available upon request]
</li>
<li>
<strong>On simple semiabelian <em>p</em>-adic Lie
algebras</strong><br>
Comm. Algebra <em>20</em>(4) (1992), 1041-1049.<br>
[<a href=
"http://dx.doi.org/10.1080/00927879208824390">published
version</a>] [preprint available upon request]
</li>
<li>
<strong>Transitive linear groups with large soluble normal
subgroups</strong><br>
Geom. Dedicata <em>38</em> (1991), 329-330.<br>
[<a href="http://dx.doi.org/10.1007/BF00181194">published
version</a>] [preprint available upon request]
</li>
</ul>
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