Some characterizations of finite simple groups

M. F. Ghasemabadi,   A. Iranmanesh

The prime graph of a finite group \(G\) is the simple undirected graph defined as follows: the vertices of this graph are the prime numbers dividing the order of \(G\), and two distinct vertices \(p\) and \(q\) are adjacent by an edge if \(G\) contains an element of order \(pq\). Up to now, this graph has been extensively studied. For instance, the structure of the prime graph of finite simple groups and their connected components have been obtained in [1,2,3]. The influence of the prime graph on the group structure of \(G\) motivates us to work on some characterizations related to this graph. In this talk, our main goal is to present our latest results on the characterization of the simple groups \(L_n(3)\), \(U_n(3)\) by prime graph and OD-characterization of the simple group \({}^2G_2(q)\).

References

1. A. S. Kondrat’ev, Prime graph components of finite simple groups, Math. Sb., 180 (1989), 787–797.
2. A. V. Vasil'ev, E. P. Vdovin, An adjacency criterion for the prime graph of a finite simple group, Algebra Logic, 44 (2005), 381–406.
3. J. S. Williams, Prime graph components of finite groups, J. Algebra, 69 (1981), 487–513.

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