The structure of groups which are rich in subnormal subgroups has been investigated by several authors. Here, we prove that if a periodic soluble group G has subnormal deviation, which means that the set of its non-subnormal subgroups satisfies a very weak chain condition, then either G is a Černikov group or all its subgroups are subnormal. It follows that if a periodic soluble group has a subnormal deviation, then its subnormal deviation is 0.
Groups with Subnormal Deviation / de Giovanni, F.; Kurdachenko, L. A.; Russo, A.. - In: MATHEMATICS. - ISSN 2227-7390. - 11:12(2023), p. 2635. [10.3390/math11122635]
Groups with Subnormal Deviation
de Giovanni F.
;
2023
Abstract
The structure of groups which are rich in subnormal subgroups has been investigated by several authors. Here, we prove that if a periodic soluble group G has subnormal deviation, which means that the set of its non-subnormal subgroups satisfies a very weak chain condition, then either G is a Černikov group or all its subgroups are subnormal. It follows that if a periodic soluble group has a subnormal deviation, then its subnormal deviation is 0.File in questo prodotto:
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