Evaluation All Possible Subgroups of a Group of Order 30 By Using Sylow’s Theorem

Evaluation All Possible Subgroups of a Group of Order 30 By Using Sylow’s Theorem
Author(s):
Sarwar Sultana
Keywords:
Dihedral group, exact sequences, split extensions of groups, Lagrangeā€™s Theorems and P- Sylowā€™s Theorems.
Abstract
In this work, we will discuss the concept of group, order of a group, along with the associated notions of automorphisms group of the dihedral groups and split extensions of groups. This work is a generalization of the Sylowā€™s Theorems. Then we find all the groups of order 30 which will give us a practical knowledge to see the applications of the Sylowā€™s Theorems. For this, we also have used some known results of Semi-direct Product of groups, some important Theorem to obtain our result. Finally, we have found all subgroups of group order 30 for Abelian and Non-abelian cases.
Article Details
Unique Paper ID: 152604 Publication Volume & Issue: Volume 8, Issue 3 Page(s): 1029 - 1034
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