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Displaying 61 – 80 of 89

The Roquette category of finite $p$ -groups

Serge Bouc (2015)

Journal of the European Mathematical Society

Let $p$ be a prime number. This paper introduces the Roquette category $ℛ_{p}$ of finite $p$ -groups, which is an additive tensor category containing all finite $p$ -groups among its objects. In $ℛ_{p}$ , every finite $p$ -group $P$ admits a canonical direct summand $\partial P$ , called the edge of $P$ . Moreover $P$ splits uniquely as a direct sum of edges of Roquette $p$ -groups, and the tensor structure of $ℛ_{p}$ can be described in terms of such edges. The main motivation for considering this category is that the additive functors from $ℛ_{p}$ to...

The Semidirect Products of Finite Cyclic Groups That Are I-E Groups.

Gary L. Peterson (1996)

Monatshefte für Mathematik

The semigroup of finite complexes of a group

Ann Miller, Franklin D. Pedersen, Walter S. Sizer (1983)

Czechoslovak Mathematical Journal

The situation of $S p_{4} (4) \cdot 2$ in the sporadic simple group He

Dieter Held (1988)

Rendiconti del Seminario Matematico della Università di Padova

The small Ree group $^{2} G_{2} (3^{2 n + 1})$ and related graph

Alireza K. Asboei, Seyed S. S. Amiri (2018)

Commentationes Mathematicae Universitatis Carolinae

Let $G$ be a finite group. The main supergraph $𝒮 (G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o (x) ∣ o (y)$ or $o (y) ∣ o (x)$ . In this paper, we will show that $G ≅^{2} G_{2} (3^{2 n + 1})$ if and only if $𝒮 (G) ≅ 𝒮 (^{2} G_{2} (3^{2 n + 1}))$ . As a main consequence of our result we conclude that Thompson’s problem is true for the small Ree group $^{2} G_{2} (3^{2 n + 1})$ .

The structure of finite p-groups: effective proof of the coclass conjectures.

Aner Shalev (1994)

Inventiones mathematicae

The Structure of the Linear Homogeneous Groups Defined by the Invariant ...........................

Leonard Eugene Dickson (1899)

Mathematische Annalen

The subgroups of $M_{24}$ , or how to compute the table of marks of a finite group.

Pfeiffer, Götz (1997)

Experimental Mathematics

The superfocal subgroup

Marian Deaconescu (1984)

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

Nel presente lavoro vengono dimostrati teoremi d'esistenza di $p$ -complementi normali nei gruppi finiti.

The symmetric group of degree six can be covered by 13 and no fewer proper subgroups.

Abdollahi, A., Ashraf, F., Shaker, S.M. (2007)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

The Tits Group as a Standard Subgroup.

Michael Aschbacher (1982)

Mathematische Zeitschrift

The uniqueness of groups of type J4.

Michael Aschbacher, Yoav Segev (1991)

Inventiones mathematicae

The weights of irreducible ${SL}_{3} (q)$ -modules in the defining characteristic.

Zavarnitsine, A.V. (2004)

Sibirskij Matematicheskij Zhurnal

Théorèmes de Sylow génériques pour les groupes réductifs sur les corps finis.

Michel Broué, Gunter Malle (1992)

Mathematische Annalen

Théorèmes sur les groupes de substitutions

Sylow (1872)

Mathematische Annalen

Theta pairs and the structure of finite groups.

Li, Xianhua, Li, Shiheng (2004)

Sibirskij Matematicheskij Zhurnal

Thompson’s conjecture for the alternating group of degree $2 p$ and $2 p + 1$

Azam Babai, Ali Mahmoudifar (2017)

Czechoslovak Mathematical Journal

For a finite group $G$ denote by $N (G)$ the set of conjugacy class sizes of $G$ . In 1980s, J. G. Thompson posed the following conjecture: If $L$ is a finite nonabelian simple group, $G$ is a finite group with trivial center and $N (G) = N (L)$ , then $G ≅ L$ . We prove this conjecture for an infinite class of simple groups. Let $p$ be an odd prime. We show that every finite group $G$ with the property $Z (G) = 1$ and $N (G) = N (A_{i})$ is necessarily isomorphic to $A_{i}$ , where $i \in {2 p, 2 p + 1}$ .

Currently displaying 61 – 80 of 89

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Displaying 61 – 80 of 89

The Roquette category of finite $p$ -groups

The Semidirect Products of Finite Cyclic Groups That Are I-E Groups.

The semigroup of finite complexes of a group

The situation of $S p_{4} (4) \cdot 2$ in the sporadic simple group He

The small Ree group $^{2} G_{2} (3^{2 n + 1})$ and related graph

The structure of finite p-groups: effective proof of the coclass conjectures.

The Structure of the Linear Homogeneous Groups Defined by the Invariant ...........................

The subgroups of $M_{24}$ , or how to compute the table of marks of a finite group.

The superfocal subgroup

The symmetric group of degree six can be covered by 13 and no fewer proper subgroups.

The Tits Group as a Standard Subgroup.

The uniqueness of groups of type J4.

The weights of irreducible ${SL}_{3} (q)$ -modules in the defining characteristic.

Théorèmes de Sylow génériques pour les groupes réductifs sur les corps finis.

Théorèmes sur les groupes de substitutions

Theta pairs and the structure of finite groups.

Thompson’s conjecture for the alternating group of degree $2 p$ and $2 p + 1$

Thompson's Problem (... =3).

Three amalgams of A_5

Three remarks on absolutely solvable groups.

Currently displaying 61 – 80 of 89