Maryam Khatami

CHARACTERIZATION BY PRIME GRAPH OF PGL(2, pk) WHERE p AND k > 1 ARE ODD

Let G be a finite group. The prime graph Γ(G) of G is defined as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, p′ are joined by an edge if there ...

Quasirecognition by prime graph of simple group D_n(3)

Let G be a nite group. The prime graph ..(G) of G is de ned as follows. The vertices of ..(G) are the primes dividing the order of G and two distinct vertices p and p�� are joined by an edge if there is an element in G of order pp��. It is proved that Dn(q), with disconnected prime graph, is quasirecognizable by their element orders. In this paper as the main result, we show that Dn(3), where n 2 fp; p+1g for an odd prime p > 3, is quasirecognizable by its prime graph.

A dual version of Huppert's conjecture on conjugacy class sizes

Abstract In [J. Algebra 344 (2011), 205–228], a conjecture of J. G. Thompson for PSLn(q) was proved. It was shown that every finite group G with the property Z(G) = 1 and cs(G) = cs(PSLn(q)) is isomorphic to PSLn(q) where cs(G) is the set of conjugacy class sizes of G. In this article we improve this result for PSL2(q). In fact we prove that if cs(G) = cs(PSL2(q)), for q > 3, then G ≅ PSL2(q) × A, where A is abelian. Our proof does not depend on the classification of finite simple groups.

Recognition of some families of finite simple groups by order and set of orders of vanishing elements

Let G be a finite group. An element g ∈ G is called a vanishing element if there exists an irreducible complex character χ of G such that χ(g)= 0. Denote by Vo(G) the set of orders of vanishing elements of G. Ghasemabadi, Iranmanesh, Mavadatpour (2015), in their paper presented the following conjecture: Let G be a finite group and M a finite nonabelian simple group such that Vo(G) = Vo(M) and |G| = |M|. Then G ≌ M. We answer in affirmative this conjecture for M = Sz(q), where q = 22n+1 and either q − 1,

On the prime graph of Dn(q) where q ∊ {2, 5}

q - \sqrt {2q} + 1

Some New Characterizations for PGL(2, q)

q−2q+1 or q +

Quasirecognition by prime graph of the simple group 2F4(q)

\sqrt {2q} + 1