A new characterization of some alternating and symmetric groups.

Khosravi, Amir; Khosravi, Behrooz

Displaying similar documents to “A new characterization of some alternating and symmetric groups.”

On connection between the structure of a finite group and the properties of its prime graph.

Vasil'ev, A.V. (2005)

Sibirskij Matematicheskij Zhurnal

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Cycles and bipartite graph on conjugacy class of groups

Bijan Taeri (2010)

Rendiconti del Seminario Matematico della Università di Padova

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OD-characterization of alternating groupsA p + d

Yong Yang, Shitian Liu, Zhanghua Zhang (2017)

Open Mathematics

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Let An be an alternating group of degree n. Some authors have proved that A10, A147 and A189 cannot be OD-characterizable. On the other hand, others have shown that A16, A23+4, and A23+5 are OD-characterizable. We will prove that the alternating groups Ap+d except A10, are OD-characterizable, where p is a prime and d is a prime or equals to 4. This result generalizes other results.

Quasirecognition by prime graph of $^{2} D_{p} (3)$ where $p = 2^{n} + 1 \geq 5$ is a prime.

Babai, A., Khosravi, B., Hasani, N. (2009)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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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, $|π (G)| \leq 8$ .

Conjugacy class lengths of metanilpotent groups

Carlo Casolo, Silvio Dolfi (1996)

Rendiconti del Seminario Matematico della Università di Padova

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Groups with the same orders of Sylow normalizers as the Mathieu groups.

Khosravi, Behrooz, Khosravi, Behnam (2005)

International Journal of Mathematics and Mathematical Sciences

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Prime-Power Factor Groups of Finite Groups. II.

George Glaubermann (1970)

Mathematische Zeitschrift

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Prime-Power Factor Groups of Finite Groups.

George Glaubermann (1968)

Mathematische Zeitschrift

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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

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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 $∣G / Z (G)∣$ .