Determination of the Degree of Homogeneity of Primitive Permutation Groups via the Socle of the Groups.

Adamu Danbaba; Sunday U. Momoh

doi:10.52589/AJMSS-84OWWYYB

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Determination of the Degree of Homogeneity of Primitive Permutation Groups via the Socle of the Groups.

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African Journal of Mathematics and Statistics Studies

Vol. 7Issue 32024pp. 190–197Published 9 September 2024

DOI 10.52589/AJMSS-84OWWYYB

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Abstract:

The nilpotentcy class for the Frobenius was determined based on the structure theorem. The socle of the groups were observed to be regular normal and elementary abelian such features were the conditions for the nilpotency classes, as they were the basis on which the socle of these groups constructed were nilpotent of some classes or order. The socle of the nilpotent groups whose structures is in conformity with D were classified based on the classification scheme for the finite primitive groups in relation to socle type.

Keywords:Frobenius groups. Socle nilpotency finite abelian regular.

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Copyrights

Authors retain copyright in their articles and have unrestricted rights to reuse, republish, archive, share, and distribute their work after publication.
All articles are published open access under the Creative Commons Attribution 4.0 International (CC BY 4.0) licence, which permits use, sharing, adaptation, distribution, and reproduction in any medium or format, including for commercial purposes, provided appropriate credit is given to the original author(s) and source.