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Supplementation in groups. (English) Zbl 0945.20016

Summary: Groups are investigated in which all subgroups, all normal subgroups, or all characteristic subgroups have a proper supplement. This supplement can be either an arbitrary subgroup, a normal or a characteristic subgroup, resulting in nine classes of groups. Properties of these classes are studied such as containment and closure properties, and characterizations for several of these classes are given.

MSC:

20E34 General structure theorems for groups
20E15 Chains and lattices of subgroups, subnormal subgroups
20E22 Extensions, wreath products, and other compositions of groups
20E07 Subgroup theorems; subgroup growth
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