Paper “A Note on Solitary Subgroups of Finite Groups” published in Comm. Algebra

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R. Esteban-Romero and Orieta Liriano

A note on solitary subgroups of finite groups.

Comm. Algebra, 44(7):2945–2952, 2016

https://doi.org/10.1080/00927872.2015.1065855

Abstract

We say that a subgroup H of a finite group G is solitary (respectively, normal solitary) when it is a subgroup (respectively, normal subgroup) of G such that no other subgroup (respectively, normal subgroup) of G is isomorphic to H. A normal subgroup N of a group G is said to be quotient solitary when no other normal subgroup K of G gives a quotient isomorphic to G/N. We show some new results about lattice properties of these subgroups and their relation with classes of groups and present examples showing a negative answer to some questions about these subgroups.

2010 Mathematics Subject Classification: 20D10, 20D30, 20F16

Keywords: Finite group, Fitting class, Formation, Quotient solitary subgroup, Solitary subgroup