On finite minimal non-nilpotent groups

[EN] A critical group for a class of groups X is a minimal non-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.

First published in Proceedings of the American Mathematical Society in volume 12, number 6:961-963 (2009), published by the American Mathematical Society http://dx.doi.org/10.1090/S0002-9939-05-07996-7 http://www.ams.org/journals/proc/2005-133-12/S0002-9939-05-07996-7/home.html