A Constructive Method for Using Known Groups as Building Blocks to form More Groups
Journal of Scientific Research and Reports · pp. 1–10 · Published 24 May 2016
10.9734/JSRR/2016/26080Abstract
In this paper, we present some methods of constructing new groups from given ones. We first examined the direct product of the finite groups Gi for n³2 and then observed that . We also established the fact that for any prime number p > 2 and any positive integer k, |U(pk)| = |U(2pk)| where U(n) is the set of all integers less than n and relatively prime to n, and finally conclude on symmetries by constructing groups and their respective subgroups, characteristics and the unique factorization of the elements.
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