On finite minimal non-nilpotent groups

Ballester-Bolinches, A.; Esteban-Romero, R.; Robinson, Derek

doi:10.1090/S0002-9939-05-07996-7

On finite minimal non-nilpotent groups
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by A. Ballester-Bolinches, R. Esteban-Romero and Derek J. S. Robinson PDF

Proc. Amer. Math. Soc. 133 (2005), 3455-3462 Request permission

Abstract:

A critical group for a class of groups $\mathfrak {X}$ is a minimal non-$\mathfrak {X}$-group. The critical groups are determined for various classes of finite groups. As a consequence, a classification of the minimal non-nilpotent groups (also called Schmidt groups) is given, together with a complete proof of Gol’fand’s theorem on maximal Schmidt groups.

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