Please use this identifier to cite or link to this item:
Title: On the Probability That an Automorphism Fixes a Group Element
Authors: Yadav, Vandana
Supervisor: Gumber, Deepak
Keywords: Commutativity degree,;Autocommutativity degree
Issue Date: 1-Aug-2019
Abstract: Let G be a finite group. Denote by P(G) the probability that two elements of G, selected randomly and with replacement, commute, and by PA(G) the probability that a randomly chosen automorphism of G fixes a randomly chosen element of G. It is known that PA(G) ≤ 5/8 for any nonabelian group. We show that PA(G) ≤ 5/8 for any noncyclic group, and then prove that this bound is not sharp. We also prove that PA(G) = P(G) if and only if Aut(G) = Autc(G), where Autc(G) denotes the group of all conjugacy class- preserving automorphisms of G. This gives another perspective on a question of Avinoam Mann.
Appears in Collections:Masters Theses@SOM

Files in This Item:
File Description SizeFormat 
dissertation.pdf532.76 kBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.