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$p$ -groups, diagonalizable automorphisms and loops

Benedetto Scimemi (1971)

Rendiconti del Seminario Matematico della Università di Padova

Parallelepipeds, nilpotent groups and Gowers norms

Bernard Host, Bryna Kra (2008)

Bulletin de la Société Mathématique de France

In his proof of Szemerédi’s Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers norm) can be defined. We focus on dimensions $2$ and $3$ and show when this possible, and describe a correspondence between the parallelepiped structures and nilpotent groups.

Partial Homogeneity in Locally Finite Groups.

R.E. Phillips, Susan.E. Schuur (1987)

Mathematische Zeitschrift

p-Brauer characters of q-Defect 0.

Wolfgang Willems, Gabriel Navarro (1994)

Manuscripta mathematica

Perfect numbers and finite groups

Tom De Medts, Attila Maróti (2013)

Rendiconti del Seminario Matematico della Università di Padova

Periodic factorization of a finite Abelian 2-group.

Corrádi, K., Szabó, S. (1999)

Rendiconti del Seminario Matematico

Periodic groups saturated by the group $U_{3} (9)$ .

Lytkina, D.V. (2007)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

Periodic groups saturated with the groups $L_{2} (p^{n})$ .

Rubashkin, A.G., Filippov, K.A. (2005)

Sibirskij Matematicheskij Zhurnal

Permutability of centre-by-finite groups

Brunetto Piochi (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $G$ be a group and $m$ be an integer greater than or equal to $2$ . $G$ is said to be $m$ -permutable if every product of $m$ elements can be reordered at least in one way. We prove that, if $G$ has a centre of finite index $z$ , then $G$ is $(1+[z/2])$ -permutable. More bounds are given on the least $m$ such that $G$ is $m$ -permutable.

Permutable Subgroups of Infinite Groups.

Stewart E. Stonehewer (1972)

Mathematische Zeitschrift

p-Nilpotence, classifying space indecomposability, and other properties of almost all finite groups.

Hans-Werner Henn, Stewart Priddy (1994)

Commentarii mathematici Helvetici

Polarities of G. Higman's symmetric design and a strongly regular graph on 176 vertices.

A.E. Brouwer (1982)

Aequationes mathematicae

Polynomial and Term Functions over Groups with Coprime Chief Factors.

Maris Ozols (1990)

Monatshefte für Mathematik

Polynomials over the permutation group of three elements

Yvona Coufalová (1980)

Archivum Mathematicum

Présentation de certains couples fischériens de type classique

M.M. Virotte-Ducharme (1993)

Bulletin de la Société Mathématique de France

Presentations of finite simple groups: a computational approach

Robert Guralnick, William M. Kantor, Martin Kassabov, Alexander Lubotzky (2011)

Journal of the European Mathematical Society

All finite simple groups of Lie type of rank $n$ over a field of size $q$ , with the possible exception of the Ree groups $^{2} G_{2} (q)$ , have presentations with at most 49 relations and bit-length $O (𝚕𝚘𝚐 n + 𝚕𝚘𝚐 q)$ . Moreover, $A_{n}$ and $S_{n}$ have presentations with 3 generators; 7 relations and bit-length $O (𝚕𝚘𝚐 n)$ , while $𝚂𝙻 (n, q)$ has a presentation with 6 generators, 25 relations and bit-length $O (𝚕𝚘𝚐 n + 𝚕𝚘𝚐 q)$ .

Prime Characters and Factorizations of Quasi-Primitive Characters.

Alexandre Turull, Pamela A. Ferguson (1985)

Mathematische Zeitschrift

Prime divisors of conjugacy class lengths in finite groups

Carlo Casolo (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show that in a finite group $G$ which is $p$ -nilpotent for at most one prime dividing its order, there exists an element whose conjugacy class length is divisible by more than half of the primes dividing $∣G / Z (G)∣$ .

Prime graph components of finite almost simple groups

Maria Silvia Lucido (1999)

Rendiconti del Seminario Matematico della Università di Padova

Primitive characters of subgroups of M-groups.

Gabriel Navarro (1995)

Mathematische Zeitschrift

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