Work

Finite Minimal Simple Groups Non-satisfying the Basis Property

Year: 2023

Type: article

Abstract: Let G be a finite group. We say that G has the Basis Property if every subgroup H of G has a minimal generating set (basis), and any two bases of H have the same cardinality. A group G is called minimal not satisfying the Basis Property if it does not satisfy the Basis Property, but all its proper subgroups satisfy the Basis Property. We prove that the following groups PSL(2, 5) ∼A5, PSL(2, 8) , are minimal groups non satisfying the Basis Property, but the groups PSL(2, 9), PSL(2, 17) and PSL(3, 4) are not minimal and not satisfying the Basis Property.

Source: European Journal of Pure and Applied Mathematics

DOI: 10.29020/nybg.ejpam.v16i3.4871

Authors: Ahmad Al Khalaf, Iman Taha

Institution: Imam Mohammad ibn Saud Islamic University

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Al-Imam Muhammad Ibn Saud Islamic University

OpenAlex ID: W4385397249

FWCI:

Cites: 13

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Related to: 10