Fixed points of automorphisms of certain finite groups

摘要

Let G = Zp 2 × Zp 3 be a finite group of order p 5 . Suppose that d is a divisor of the order of group G. In this article, we enumerated all automorphisms of G fixing d elements of G and denote them by Θ(G, d), we characterize the automorphism group as 2 by 2 matrices with entries are from finite groups. We also compute a formula for Θ(Q4p, d), where Q4p is the dicyclic group of order 4p, p is an odd prime and the divisor d ∈ {1, 2, 4, p, 2p, 4p}.