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On stabilizers of suites in groups of Alëshin type. (Russian) Zbl 0703.20035

The definition of a group of Alëshin type or, shortly, an AT-group was given by the author earlier [ibid. 40, No.5, 572-589 (1986; Zbl 0614.20019)]. Stabilizers of finite and infinite suites in AT-groups are considered in the present article. Conditions are indicated when the stabilizers of suites coincide, and their normal closure, normalizers and indices in the group are determined. It is proved also that the stabilizers of infinite suites in some AT-groups are self-normalizing subgroups of infinite index, and all subgroups containing them properly are of finite index. Finally, an example of a countable locally nilpotent AT-group not satisfying the normalizer condition is constructed.
Reviewer: Yu.I.Merzlyakov

MSC:

20F50 Periodic groups; locally finite groups
20F19 Generalizations of solvable and nilpotent groups
20E07 Subgroup theorems; subgroup growth

Citations:

Zbl 0614.20019
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