Journal of Integer Sequences, Vol. 20 (2017), Article 17.8.1

Bases in Dihedral and Boolean Groups


Volodymyr Gavrylkiv
Vasyl Stefanyk Precarpathian National University
Department of Algebra and Geometry
Shevchenko str., 57
Ivano-Frankivsk
Ukraine

Abstract:

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.


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Received 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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