Configuration of Groups Containing Generalized Normal Subgroups

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Published: Sep 2, 2024
DOI: https://doi.org/10.29070/8e1dwh50
Keywords:
Commutator, Abelian subgroups, Formalizers, Normal Subgroup, Finite subgroups

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Authors

Mohd Haqnawaz Khan

Research Scholar (Mathematics), Madhyanchal Professional University, Bhopal, M.P.

Dr. Devendra Gautam

Research Supervisor, Madhyanchal Professional University, Bhopal, M.P.

Abstract

This paper aims to identify unique symmetric presentation of normal subgroups. It is often observed that a subgroup X of a group G is considered almost normal if the index |G:NG(X)| is finite, while X is termed nearly normal if it possesses a finite index in its normal closure . We introduce some concepts related to commutators and abelian subgroups. This paper explores the structure of groups in which every infinite subgroup is either almost normal or nearly normal.

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Vol. 21 No. 2 (2024): Journal of Advances in Science and Technology (JAST)

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