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Title

SOME FINITE GROUPS WITH DIVISIBILITY GRAPH CONTAINING NO TRIANGLES

Pages

 Start Page 57 | End Page 65

Abstract

 Let G be a nite group. The graph D(G) is a divisibility graph of G. Its vertex set is the non-central conjugacy class sizes of G and there is an edge between vertices a and b if and only if ajb or bja. In this paper, we investigate the structure of the divisibility graph D(G) for a non-solvable group with  ∗ (G) = 2, a nite simple group G that satis es the one-prime power hypothesis, a group of type(A), (B) or (C) and certain metacyclic p􀀀 groups and a minimal non-metacyclic p􀀀 group where p is a prime number. We will show that the divisibility graph D(G) for all of them has no triangles.

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