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2014•AIP conference proceedingsRequires access

On some relations of subnormal subgroups and semipermutability of a finite group

Doaa Mustafa Al-Sharo, Hajar Sulaiman

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Abstract

All groups considered here are finite. A group G is said to be a BT-group if semipermutability is a transitive relation in G. A group G is called an SP-group if all subnormal subgroups of G are semipermutable in G. The concept of SP-groups was introduced by Ragland. In this paper we will show some known theorems and give an example of an SP-group of the smallest order which is not a BT-group.

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What this paper is about

All groups considered here are finite. A group G is said to be a BT-group if semipermutability is a transitive relation in G. A group G is called an SP-group if all subnormal subgroups of G are semipermutable in G. The concept of SP-groups was introduced by Ragland. In this paper we will show some known theorems and give an example of an SP-group of the smallest order which is not a BT-group.

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Available abstract

All groups considered here are finite. A group G is said to be a BT-group if semipermutability is a transitive relation in G. A group G is called an SP-group if all subnormal subgroups of G are semipermutable in G. The concept of SP-groups was introduced by Ragland. In this paper we will show some known theorems and give an example of an SP-group of the smallest order which is not a BT-group.

Key concepts: Group (periodic table), Transitive relation, Finite group, Mathematics, Order (exchange), Combinatorics, Relation (database), Group action

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