Received:
31 October 2016
Accepted:
17 November 2016
Published:
27 December 2016
Abstract: In this article, the connections between symmetric groups and the matrix groups
are investigated for exploring the application of Cayley’s theorem in finite group theory. The exact forms of the permutation groups isomorphic to the groups
,
and
are obtained within the frame of the group-theoretical approach. The results are analyzed in detail and compared with that from Cayley's theorem. It shows that the orders of the symmetric groups in present formulas are less than the latter. Various directions for future investigations on the research results have been pointed out.