Abnormal, Pronormal, Contranormal, and Carter Subgroups in Some Generalized Minimax Groups

ABSTRACT

Some properties of abnormal and pronormal subgroups in generalized minimax groups are considered. For generalized minimax groups (not only periodic) whose locally nilpotent residual is nilpotent and satisfies Min-G the existence of Carter subgroups and their conjugations have been proven. Some generalizations of results of J. Rose on abnormal and contranormal subgroups have been also obtained.

Key Words:

• Abnormal subgroups
• Carter subgroups
• Contranormal subgroups
• Descendant subgroups
• Pronormal subgroups

Mathematics Subject Classification:

• 20E34
• 20F19
• 20F22

ACKNOWLEDGMENTS

The authors are very thankful to the referee for the very thoughtful, detailed comments, which significantly improved the material exposition. This research was supported by Proyecto BFM2001–2452 of CYCIT (Spain) and Proyecto 100/2001 of Gobierno de Aragon (Spain).

Communicated by A. Olshanskiy.