JP Journal of Algebra, Number Theory and Applications
Volume 40, Issue 6, Pages 1029 - 1042
(December 2018) http://dx.doi.org/10.17654/NT040061029 |
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CLASSIFYING NONEQUIVALENT PRESENTATIONS OF FINITE GROUPS - THE CASE OF DICYCLIC GROUPS
Peteris Daugulis
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Abstract: The problem of classifying equivalence classes of presentations up to isomorphism of Cayley graphs is considered in this article in the case of dicyclic groups. This case is chosen as a starting point for solving this problem because the number of equivalence classes of presentations is uniformly bounded - it is a “finite type” case. We find all equivalence classes of presentations of dicyclic groups having two generators. For the dicyclic group of order 4n apart from the classical presentation with order multiset {{2n, 4}} for all n there are presentations with order multiset {{4, 4}}. If n is odd there is an additional presentation having elements with order multiset {{n, 4}}. These results may be used in characterizing group structure and properties. |
Keywords and phrases: group presentation, Cayley graph, dicyclic group, generalized quaternion group.
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