Journal Article

A note on solitary subgroups of finite groups

Esteban-Romero, R.

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Liriano Castro, Orieta
Fecha de publicaciónRevistaDOI
2016
Communications in Algebra  
10.1080/00927872.2015.1065855
Resumen
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.