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Journal:
Acta Mathematica Scientia

Issue Date:
2011

Abstract(summary):

Let G be a finite group and pi(G) = {p1, p2,..., p(k)} be the set of the primes dividing the order of G. We define its prime graph Gamma(G) as follows. The vertex set of this graph is pi(G), and two distinct vertices p, q are joined by an edge if and only if pq is an element of pi(e)(G). In this case, we write p similar to q. For p is an element of pi(G), put deg(p) := vertical bar{q is an element of pi(G)vertical bar p similar to q}vertical bar, which is called the degree of p. We also define D(G) := (deg(p(1)), deg(p(2)),..., deg(p(k))), where p(1) < p(2) < ... < p(k), which is called the degree pattern of G. We say a group G is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups with the same order and degree pattern as G. Specially, a 1-fold OD-characterizable group is simply called an OD-characterizable group. Let L := U(6)(2). In this article, we classify all finite groups with the same order and degree pattern as an almost simple groups related to L. In fact, we prove that L and L.2 are OD-characterizable, L.3 is 3-fold OD-characterizable, and L.S(3) is 5-fold OD-characterizable.

Page:
441-450

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