Groups in Which the Normal Closures of Cyclic Subgroups Have Bounded Finite Hirsch–Zaitsev Rank
Journal Article
·
· Journal of Mathematical Sciences
In this paper, we study generalized soluble groups with restriction on normal closures of cyclic subgroups. A group G is said to have finite Hirsch–Zaitsev rank if G has an ascending series whose factors are either infinite cyclic or periodic and if the number of infinite cyclic factors is finite. It is not hard to see that the number of infinite cyclic factors in each of such series is an invariant of a group G. This invariant is called the Hirsch–Zaitsev rank of G and will be denoted by r{sub hz}(G). We study the groups in which the normal closure of every cyclic subgroup has the Hirsch–Zaitsev rank at most b (b is some positive integer). For some natural restrictions we find a function k{sub 1}(b) such that r{sub hz}([G/Tor(G),G/Tor(G)]) ≤ k{sub 1}(b).
- OSTI ID:
- 22773909
- Journal Information:
- Journal of Mathematical Sciences, Journal Name: Journal of Mathematical Sciences Journal Issue: 1 Vol. 233; ISSN JMTSEW; ISSN 1072-3374
- Country of Publication:
- United States
- Language:
- English
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