Many Frobenius complements have even order

2021/02/06 by Brown, Ron
#11N45 (Secondary) #20E99 (Primary) 11N01 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2102.03460

Abstract

The theory of Frobenius groups with Frobenius complements of even order largely reduces to tractable algebraic number theory. If we consider only Frobenius complements with an upper bound s on the number of distinct primes dividing the order of their commutator subgroups, then the proportion of these with odd order is less than 1/2^s. A positive lower bound is also given.

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