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


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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