Properties of Quasinormal Groups (PQG)
Main Article Content
Abstract
The A subgroup of a group is termed permutable (or quasinormal) in if it satisfies the following equivalent conditions:
- For any subgroup of , (the product of subgroups and ) is a group
- For any subgroup of , , i.e., and are permuting subgroups.
- For every , permutes with the cyclic subgroup generated by . In symbols, for every and , there exists and an integer such that .
We say that G=AB is the mutually permutable product of the subgroups A and B if A permutes with every subgroup of B and B permutes with every subgroup of A. We say that the product is totally permutable if every subgroup of A permutes with every subgroup of B.
In this paper we prove the following theorem
Let G=AB be the mutually permutable product of the super soluble subgroups A and B. If CoreG(A∩B)=1, then G is super soluble.
Article Details
How to Cite
Dixit, K. and Behnam Razzaghmanesshi (2020) “Properties of Quasinormal Groups (PQG)”, International Journal of Current Research in Science and Technology, 6(08). doi: 10.57181/ijcrst.v6i08.30.
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Original Research Articles