Displaying similar documents to “Cycles and bipartite graph on conjugacy class of groups”

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.

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 ∼ 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 ≤ 8 .