D-sets Generated by a Subset of a Group

Michael Patula Baldado Jr., Cristopher John Salvador Rosero

Abstract

A subset D of a group G is a D-set if every element of G, not in D, has its inverse in D. Let A be a non-empty subset of G. A smallest D-set of G that contains A is called a D-set generated by A, denoted by <A>. Note that <A> may not be unique. This paper characterized sets A with unique <A> and sets whose number of generated D-sets is equal to the index minimum.

Keywords

groups, D-sets, index minimum

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