Prime divisors of conjugacy class lengths in finite groups

Carlo Casolo

Displaying similar documents to “Prime divisors of conjugacy class lengths in finite groups”

Conjugacy class lengths of metanilpotent groups

Carlo Casolo, Silvio Dolfi (1996)

Rendiconti del Seminario Matematico della Università di Padova

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Groups in which the prime graph is a tree

Maria Silvia Lucido (2002)

Bollettino dell'Unione Matematica Italiana

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The prime graph $Γ (G)$ of a finite group $G$ is defined as follows: the set of vertices is $π (G)$ , the set of primes dividing the order of $G$ , and two vertices $p$ , $q$ are joined by an edge (we write $p \sim q$ ) if and only if there exists an element in $G$ of order $p q$ . We study the groups $G$ such that the prime graph $Γ (G)$ is a tree, proving that, in this case, $|π (G)| \leq 8$ .

Finite groups with an automorphism of prime order whose fixed points are in the Frattini of a nilpotent subgroup

Anna Luisa Gilotti (1990)

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

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In this paper it is proved that a finite group G with an automorphism $α$ of prime order r, such that $C_{G} (α) = 1$ is contained in a nilpotent subgroup H, with $(|H|, r) = 1$ , is nilpotent provided that either $|H|$ is odd or, if $|H|$ is even, then r is not a Fermât prime.

The Hughes subgroup

Robert Bryce (1994)

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

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Let $G$ be a group and $p$ a prime. The subgroup generated by the elements of order different from $p$ is called the Hughes subgroup for exponent $p$ . Hughes [3] made the following conjecture: if $H_{p} (G)$ is non-trivial, its index in $G$ is at most $p$ . There are many articles that treat this problem. In the present Note we examine those of Strauss and Szekeres [9], which treats the case $p = 3$ and $G$ arbitrary, and that of Hogan and Kappe [2] concerning the case when $G$ is metabelian, and $p$ arbitrary. A common...