On the structure of groups, whose subgroups are either normal or core-free

Leonid A. Kurdachenko, A.A. Pypka, Igor Ya. Subbotin

Type: Article

Publication Date: 2019-04-01

Citations: 1

DOI: https://doi.org/10.15407/dopovidi2019.04.017

Abstract

On the structure of groups, whose subgroups are either normal or core-free Presented by Corresponding Member of the NAS of Ukraine V.P. MotornyiWe investigate the influence of some natural types of subgroups on the structure of groups.A subgroup H of the group G is called core-free if Core ( ) G H = 〈1〉.We study the groups, in which every subgroup is either normal or core-free.More precisely, we obtain the structures of monolithic and non-monolithic groups with this property.

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Reports of the National Academy of Sciences of Ukraine - View - PDF
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Works Cited by This (6)

Action	Title	Year	Authors
+	Groups with all subgroups either subnormal or self-normalizing	2004	Leonid A. Kurdachenko Howard L. Smith
+	Groups with only normal and abnormal subgroups	1974	Abiabdollah Fattahi
+	A note on subnormal and abnormal chains	1975	Gary L. Ebert Steven Bauman
+	Groups whose all subgroups are ascendant or self-normalizing	2011	Leonid A. Kurdachenko Javier Otal Alessio Russo Giovanni Vincenzi
+	The groups whose cyclic subgroups are either ascendant or almost self-normalizing	2016	Leonid A. Kurdachenko A.A. Pypka N. N. Semko
+	Finite groups in which the cores of every non-normal subgroups are trivial	2018	Libo Zhao Yangming Li Lü Gong