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arXiv · 1607.06418

Group bases for some solvable groups and semidirect products

Bret Benesh·Jason Lutz
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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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Bret Benesh, Jason Lutz. 2016-07-21. Group bases for some solvable groups and semidirect products. https://arxiv.org/abs/1607.06418

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