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.


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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