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In this paper as the main result, we determine finite groups with the same prime graph as the automorphism group of a sporadic simple group, except $J_{2}$ .

On the product of two n-decomposable soluble groups.

L. S. Kazarin, A. Martínez-Pastor, M. D. Pérez-Ramos (2009)

Publicacions Matemàtiques

On the projective characters in characteristic 2 of the groups $S u z (2^{m})$ and $S p_{4} (2^{n})$

Leonard Chastkofsky, Walter Feit (1980)

Publications Mathématiques de l'IHÉS

On the Projectives of a Group Algebras.

Wolfgang Willems (1980)

Mathematische Zeitschrift

On the proof of a theorem of Pálfy.

Dobson, Edward (2006)

The Electronic Journal of Combinatorics [electronic only]

On the rarity of quasinormal subgroups

John Cossey, Stewart Stonehewer (2011)

Rendiconti del Seminario Matematico della Università di Padova

On the recognizability of some projective general linear groups by the prime graph

Masoumeh Sajjadi (2022)

Commentationes Mathematicae Universitatis Carolinae

Let $G$ be a finite group. The prime graph of $G$ is a simple graph $Γ (G)$ whose vertex set is $π (G)$ and two distinct vertices $p$ and $q$ are joined by an edge if and only if $G$ has an element of order $p q$ . A group $G$ is called $k$ -recognizable by prime graph if there exist exactly $k$ nonisomorphic groups $H$ satisfying the condition $Γ (G) = Γ (H)$ . A 1-recognizable group is usually called a recognizable group. In this problem, it was proved that $PGL (2, p^{α})$ is recognizable, if $p$ is an odd prime and $α > 1$ is odd. But for even $α$ , only the recognizability...

On the regular Sylow $p$ -subgroups of Chevalley groups over $Z_{p^{m}}$ .

Kolesnikov, S.G. (2006)

Sibirskij Matematicheskij Zhurnal

On the Shemetkov problem for Fitting classes.

Guo, Wenbin, Li, Baojun (2007)

Beiträge zur Algebra und Geometrie

On the solvability of commutative loops and their multiplication groups

Kari Myllylä, Markku Niemenmaa (1999)

Commentationes Mathematicae Universitatis Carolinae

We investigate the situation when the inner mapping group of a commutative loop is of order $2 p$ , where $p = 4 t + 3$ is a prime number, and we show that then the loop is solvable.

On the Splitting of Extensions by a Group of Prime Order.

John S. Rose (1970)

Mathematische Zeitschrift

On the Structure of 2-Local Subgroups in Finite Groups.

Franz Timmesfeld (1978)

Mathematische Zeitschrift

On the structure of finite loop capable Abelian groups

Markku Niemenmaa (2007)

Commentationes Mathematicae Universitatis Carolinae

Loop capable groups are groups which are isomorphic to inner mapping groups of loops. In this paper we show that abelian groups $C_{p}^{k} \times C_{p} \times C_{p}$ , where $k \geq 2$ and $p$ is an odd prime, are not loop capable groups. We also discuss generalizations of this result.

On the structure of finite loop capable nilpotent groups

Miikka Rytty (2010)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either $C_{p^{k}} \times C_{p^{l}}$ , $k > l \geq 0$ as the Sylow $p$ -subgroup for some odd prime $p$ or the group of quaternions as the Sylow $2$ -subgroup may not be loop capable.

On the structure of solvable $n C$ -groups

Homer Bechtell (1972)

Rendiconti del Seminario Matematico della Università di Padova

On the structure of the groups related to the 3-local subgroups of the finite simple groups of Ree type.

Robert W. van der Waall (1979)

Journal für die reine und angewandte Mathematik

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