Author/Authors :
Rezaeezadeh، G. R. نويسنده Faculty of Mathematical Sciences, Shahrekord University, P.O.Box:115, Shahrekord, Iran. , , Darafsheh، M. R. نويسنده School of mathematics, College of Science, University of tehran, Tehran, Iran. , , Bibak، M. نويسنده Faculty of Mathematical Sciences, Shahrekord University, P.O.Box:115, Shahrekord, Iran. , , Sajjadi، M. نويسنده niversity of Shahrekord ,
Abstract :
Let G be a finite group and ?e(G) be the set of orders of all
elements in G. The set ?e(G) determines the prime graph (or GrunbergKegel graph) ?(G) whose vertex set is ?(G). The set of primes dividing
the order of G, and two vertices p and q are adjacent if and only if
pq ? ?e(G). The degree deg(p) of a vertex p ? ?(G), is the number of
edges incident on p. Let ?(G) = {p1, p2, ..., pk} with p1 < p2 < ... < pk.
We define D(G) := (deg(p1), deg(p2), ..., deg(pk)), which is called the
degree pattern of G. The group G is called k-fold OD-characterizable
if there exist exactly k non-isomorphic groups M satisfying conditions
|G| = |M| and D(G) = D(M). Usually a 1-fold OD-characterizable
group is simply called OD-characterizable. In this paper, we classify all
finite groups with the same order and degree pattern as an almost simple
groups related to D4(4).
