Conjugate p-elements of Full Support that Generate the Wreath Product Cp wr Cp

Ward, David (2014) Conjugate p-elements of Full Support that Generate the Wreath Product Cp wr Cp. [MIMS Preprint]

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Abstract

For a symmetric group G:=Sym(n) and a conjugacy class X of involutions in G, it is known that if the class of involutions does not have a unique fixed point, then - with a few small exceptions - given two elements a,x in X, either <a,x> is isomorphic to the dihedral group D8, or there is a further element y in X such that <a,y> and <x,y> are both isomorphic to D8 (P. Rowley and D. Ward, On pi-Product Involution Graphs in Symmetric Groups. MIMS ePrint, 2014). One natural generalisation of this to p-elements is to consider when two conjugate p-elements generate a wreath product of two cyclic groups of order p. In this paper we give a necessary and sufficient condition for this in the case that our p-elements have full support.

Item Type: MIMS Preprint
Additional Information: Submitted to The Electronic Journal of Linear Algebra.
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 05 Combinatorics
MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User: Mr David Ward
Date Deposited: 20 Jun 2014
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2147

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