Groups with finitely many conjugacy classes of non-normal subgroups of infinite rank

Maria De Falco; Francesco de Giovanni; Carmela Musella

doi:10.4064/cm131-2-6

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Groups with finitely many conjugacy classes of non-normal subgroups of infinite rank

Maria De Falco Francesco de Giovanni Carmela Musella

Year: 2013 Journal: Colloquium Mathematicum Vol: 131 (2)Pages: 233-239 Publisher: Polish Academy of Sciences

DOI: 10.4064/cm131-2-6

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Abstract

It is proved that if a locally soluble group of infinite rank has only finitely many non-trivial conjugacy classes of subgroups of infinite rank, then all its subgroups are normal.

Keywords:

Mathematics Conjugacy class Rank (graph theory) Finitely-generated abelian group Combinatorics Normal subgroup Pure mathematics Group (periodic table)

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Finite Group Theory Research

Physical Sciences → Mathematics → Discrete Mathematics and Combinatorics

Rings, Modules, and Algebras

Physical Sciences → Mathematics → Algebra and Number Theory

Groups with finitely many conjugacy classes of non-normal subgroups of infinite rank

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