Groups with finiteness conditions on some subgroup systems: a contemporary stage. (English) Zbl 1199.20051

Dixon, Martyn R.; Subbotin, Igor Ya.

Algebra Discrete Math. 2009, No. 4, 29-54 (2009).

Summary: This paper gives a brief historical survey of results in which certain systems of subgroups of a group satisfy various finiteness conditions.

MSC:

20E15	Chains and lattices of subgroups, subnormal subgroups
20E07	Subgroup theorems; subgroup growth
20F19	Generalizations of solvable and nilpotent groups
20F22	Other classes of groups defined by subgroup chains

Keywords:

infinite groups; finiteness conditions; subnormality; almost normality; commutativity; maximal condition; minimal condition; series of subgroups