Abstract
Baer [2] and Neumann [5] have discussed groups in which there is a
limitation on the number of conjugates which an element may have. For a
given group G, let H1 be the set of all elements of G which have
only a finite number of conjugates in G, let H2 be the set of
those elements of G, the conjugates of each of which lie in only a finite
number of cosets of H1 in G; and in this fashion define
H3, H4, …. We shall show that the Hi are
strictly characteristic subgroups of G.
Publisher
Canadian Mathematical Society
Cited by
11 articles.
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1. Almost group theory;Journal of Algebra;2020-08
2. Strong amenability and the infinite conjugacy class property;Inventiones mathematicae;2019-07-13
3. A note on FC-nilpotency;Journal of Algebra and Its Applications;2018-08-23
4. Definable envelopes in groups having a simple theory;Journal of Algebra;2017-12
5. A Fitting theorem for simple theories;Bulletin of the London Mathematical Society;2016-03-30