Bases in dihedral and Boolean groups

Summary

Summary: A subset $B$ of a group $G$ is called a $basis$ of $G$ if $G = B^{2}$. The smallest cardinality of a basis of $G$ is called the basis size of $G$. We prove upper bounds for basis sizes of dihedral and Boolean groups. We find a lower bound for the basis size of a Boolean group. We also calculate basis sizes for dihedral and Boolean groups of small orders.

Mathematics Subject Classification

05B10, 05E15, 20D60

Keywords/Phrases

dihedral group, Boolean group, basis, basis size, basis characteristic