TY  - JOUR
AU  - Rashid, S. 
AU  - Sarmin, N. H. 
AU  - Erfanian, A. 
AU  - Ali, N. M. Mohd 
PY  - 2012
TI  - On the Derived Subgroups of Some Finite Groups
JF  - Journal of Mathematics and Statistics
VL  - 8
IS  - 1
DO  - 10.3844/jmssp.2012.111.113
UR  - https://thescipub.com/abstract/jmssp.2012.111.113
AB  - 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.