CHAIN CONDITIONS FOR SUBNORMAL SUBGROUPS OF INFINITE ORDER OR INDEX

Abstract

A group G is said to satisfy max-∞s if each nonempty set of infinite subnormal subgroups of G has a maximal element. A group G is said to satisfy min-∞s if each nonempty set of subnormal subgroups of G with infinite index has at least one minimal element.

Groups with max-∞s or min-∞s are the subject of this paper. Solvable groups with max-∞s or min-∞s are examined in detail and structure theorems are given. We then show that subsolvable groups with max-∞s or min-∞s are solvable.

ACKNOWLEDGMENTS

The author would like to thank Professor Derek J. S. Rob inson for his guidance and support.