On the order of a group of even order
Copyright policy )On the order of a group of even order
Let \(G\) be a group of even order with a unique conjugacy class of involutions. In the paper under review the authors provide an upper bound for the order of \(G\) in terms of the centralizer \(H=C_G(t)\) of an involution \(t\) in \(G\). As an application the authors provide examples of sporadic simple groups, the groups \(Ly\) and \(Th\), whose orders could be found using the upper bound obtained in this paper.
- THE OHIO STATE UNIVERSITY United States
- University of Tsukuba Japan
- The Ohio State University United States
Algebra and Number Theory, centralizers of involutions, finite groups, Sporadic simple group, groups of even order, sporadic simple groups, Finite group, order formulae, Order formula, Arithmetic and combinatorial problems involving abstract finite groups, Simple groups: sporadic groups
Algebra and Number Theory, centralizers of involutions, finite groups, Sporadic simple group, groups of even order, sporadic simple groups, Finite group, order formulae, Order formula, Arithmetic and combinatorial problems involving abstract finite groups, Simple groups: sporadic groups
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