Journal of Mathematics and Statistics

On the Derived Subgroups of Some Finite Groups

S. Rashid, N. H. Sarmin, A. Erfanian and N. M. Mohd Ali

DOI : 10.3844/jmssp.2012.111.113

Journal of Mathematics and Statistics

Volume 8, Issue 1

Pages 111-113

Abstract

Problem statement: In this study we focus on the derived subgroup of nonabelian 3-generator groups of order p3q, where p and q are distinct primes and p < q. Our main objective is to compute the derived subgroup for these groups up to isomorphism. Approach: In a group G, the derived subgroup G' = [G, G] is generated by the set of commutators of G, K (G) = {[x, y]| x, y ∈ G} and introduced by Dedekind. The relations of the group are used to compute the derived subgroup. Results: The results show that the derived subgroup of nonabelian 3-generator groups of order p3q is a cyclic group, Q8 or A4. Conclusion/Recommendations: The problem can be considered to compute the derived subgroup of these groups without the use of the relations.

Copyright

© 2012 S. Rashid, N. H. Sarmin, A. Erfanian and N. M. Mohd Ali. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.