A counterexample to Herzog's Conjecture on the number of involutions

2018/02/20 by Zarrin, Mohammad
#20D06 #20D60 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1802.08162

Abstract

In 1979, Herzog put forward the following conjecture: if two simple groups have the same number of involutions, then they are of the same order. We give a counterexample to this conjecture.

Related

• Commuting Involutions in Finite Simple Groups
• Asymptotics of the number of involutions in finite classical groups
• Finite groups with many involutions
• The involution width of finite simple groups
• Generation of finite simple groups by an involution and an element of prime order