Journal of Mathematics and Statistics, Volume (8), No (1), Year (2012-1) , Pages (111-113)

Title : ( On the Derived Subgroups of Some Finite Groups )

Authors: S. Rashid , N. H. Sarmin , Ahmad Erfanian , N. M. Mohd Ali ,

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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 Î 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.

Keywords

, Derived subgroup, sylow theorems, finitely generated
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@article{paperid:1026361,
author = {S. Rashid and N. H. Sarmin and Erfanian, Ahmad and N. M. Mohd Ali},
title = {On the Derived Subgroups of Some Finite Groups},
journal = {Journal of Mathematics and Statistics},
year = {2012},
volume = {8},
number = {1},
month = {January},
issn = {1549-3644},
pages = {111--113},
numpages = {2},
keywords = {Derived subgroup; sylow theorems; finitely generated group},
}

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%0 Journal Article
%T On the Derived Subgroups of Some Finite Groups
%A S. Rashid
%A N. H. Sarmin
%A Erfanian, Ahmad
%A N. M. Mohd Ali
%J Journal of Mathematics and Statistics
%@ 1549-3644
%D 2012

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