Bases in Dihedral and Boolean Groups
Vasyl Stefanyk Precarpathian National University
Department of Algebra and Geometry
Shevchenko str., 57
A subset B of a group G is called a basis
of G if G = B2.
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.
Full version: pdf,
April 18 2017; revised versions received April 20 2017; June 24 2017; June 26 2017; July 6 2017.
Published in Journal of Integer Sequences, July 31 2017.
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