Group bases for some solvable groups and semidirect products

2016/07/21 by Bret J. Benesh, Bret Benesh, Benesh, Bret +2
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Finite Group Theory Research #graph theory and CDMA systems #math.GR #msc:20E99

paper · pdf · doi:10.48550/arxiv.1607.06418

2 pages

arxiv created 2016/07/21 · arxiv updated 2016/07/22

Abstract

A set B is a basis for a vector space V if every element of V can be uniquely written as a linear combination of the elements of B. There is a similar definition of a basis for a finite group. We show that certain semidirect products of finite groups---including all semidirect products of finite abelian groups---have bases; any group of order m or 2m for odd, cube-free m has a basis; and the quaternions do not have a basis.

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