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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Vasil'ev, A.V. (2005)
Sibirskij Matematicheskij Zhurnal
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Bijan Taeri (2010)
Rendiconti del Seminario Matematico della Università di Padova
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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.
Babai, A., Khosravi, B., Hasani, N. (2009)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Maria Silvia Lucido (2002)
Bollettino dell'Unione Matematica Italiana
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The prime graph of a finite group is defined as follows: the set of vertices is , the set of primes dividing the order of , and two vertices , are joined by an edge (we write ) if and only if there exists an element in of order . We study the groups such that the prime graph is a tree, proving that, in this case, .
Carlo Casolo, Silvio Dolfi (1996)
Rendiconti del Seminario Matematico della Università di Padova
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Khosravi, Behrooz, Khosravi, Behnam (2005)
International Journal of Mathematics and Mathematical Sciences
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George Glaubermann (1970)
Mathematische Zeitschrift
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George Glaubermann (1968)
Mathematische Zeitschrift
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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 which is -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 .