• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2023, Volume: 16, Issue: 25, Pages: 1872-1876

Original Article

Strong Gamma Group

Received Date:01 June 2023, Accepted Date:01 June 2023, Published Date:27 June 2023


Objectives: The primary goal of this study is to present the concept of a strong G 􀀀 group as a generalization of G 􀀀 group. Methods and Findings: We have investigated some of the properties of the G􀀀 group and extended it to introduce the idea of a strong G􀀀 group. Novelty: Every strong G􀀀 group is a G 􀀀 group, but not all G􀀀 groups are strong G􀀀 groups. Further if G is a non-empty G􀀀 semigroup and for all a;b e G, the equations aax = b and yaa = b for all x; y e G and for all a e G have unique solutions in G, then G is a strong G􀀀 group. Also, we characterize that non-empty subsetH of a strong G􀀀 groupG is a strong G􀀀 subgroup if and only if for all a;b eH;aac e H for all a e G where c is strong inverse of b in G. Finally, we prove that the intersection of two strong G􀀀 subgroups is again a strong G􀀀 subgroup and the center of strong G􀀀 group C(G) is also a G􀀀 subgroup.

Keywords: Semigroup; Strong G 􀀀group; Strong G 􀀀subgroup; Centre of G 􀀀group


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3) Kapil VS, Kumar A, Sharma TR. Some results of a gamma group-I. AIP Conference Proceedings. 2022. Available from: https://doi.org/10.1063/5.0095276.


© 2023 Singh Kapil et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)


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