Finite minimal simple implies 2-generated

This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., finite minimal simple group) must also satisfy the second group property (i.e., 2-generated group)
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History

This fact was first proved by Thompson as a consequence of the classification of finite minimal simple groups. It was later proved by Paul Flavell without using the classification.

Statement

Any finite minimal simple group is a 2-generated group: it has a generating set of size two.

Related facts

• Finite simple implies 2-generated
• Finite almost simple implies 3-generated

Facts used

1. Classification of finite minimal simple groups

References

• Nonsolvable finite groups all of whose local subgroups are solvable by John Griggs Thompson, Bulletin of the American Mathematical Society, ISSN 10889485 (electronic), ISSN 02730979 (print), Volume 74, Page 383 - 437(Year 1968): In this paper (appearing across multiple issues of the Pacific Journal of Mathematics), Thompson classified all N-groups.^{WeblinkMore info}