Groups with all non-subnormal subgroups of finite rank

Kurdachenko, Leonid A.; Soules, Panagiotis

doi:10.1017/cbo9780511542787.006

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Theorem 1 [5 Theorem 122] Let G Be a Group Whose Non-subn1

Theorem 2 Let G Be a Locally Soluble-by-finite Group In Whi1

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Cited by 2 publications

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“…This result generalizes to some extent the well-known theorem of Roseblade [9] that a group in which every subgroup is subnormal of bounded defect is nilpotent (of bounded class). In the present article we return to the theme of [5] and establish the following improvement on Theorem 1 above.…”

Section: Theorem 1 [5 Theorem 122] Let G Be a Group Whose Non-subnmentioning

confidence: 85%

“…As noted in [5], the solubility of G is a reasonable hypothesis in the statement of Theorem 1, since a group with all subgroups subnormal is in any case soluble, a remarkable result due to Möhres [6]. On the other hand, such a group need not be nilpotent, as the famous Heineken-Mohamed examples [4] indicate -these groups have trivial centre and all subgroups subnormal.…”

Section: Theorem 2 Let G Be a Locally Soluble-by-finite Group In Whimentioning

confidence: 88%

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Groups in Which All Subgroups of Infinite Rank Are Subnormal

Kurdachenko

Smith²

2004

Glasgow Math. J.

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Abstract. Let G be a locally soluble-by-finite group in which every nonsubnormal subgroup has finite rank. It is proved that either G has finite rank or G is soluble and locally nilpotent (and even a Baer group). On the other hand, a group G is constructed that has infinite rank and satisfies the given hypothesis, but does not have every subgroup subnormal.2000 Mathematics Subject Classification. 20E15, 20F19.

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Section: Theorem 1 [5 Theorem 122] Let G Be a Group Whose Non-subnmentioning

confidence: 85%