Groups With the Same Prime Graph as a CIT Simple Group

• Autores: Behrooz Khosravi, Behman Khosravi, Bahman Khosravi
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 4, 2007, págs. 967-977
• Idioma: inglés
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• Resumen

  • Let G be a finite group. The prime graph of G is the graph whose vertex set is the set of all prime divisors of |G|, and two distinct primes p and q are joined by an edge if and only if G contains an element of order pq. A group M is called a CIT group or a C22 group if M is of even order and the centralizer of any involution is a 2-group. In this paper we determine finite groups G such that their prime graph is the same prime graph of M, where M is a CIT simple group. As a consequence of this result, we prove that if p>7 is a Mersenne prime or a Fermat prime, then PSL(2,p) is uniquely determined by its prime graph. Also we prove a few results by using the main theorem.