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A note on solitary subgroups of finite groups. (English) Zbl 1351.20007
A subgroup $$H$$ of a finite group $$G$$ is called 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 if no other normal subgroup $$K$$ of $$G$$ has a quotient isomorphic to $$G/N$$. In this paper, some new results about lattice properties of these subgroups and their relation with classes of groups are given. The authors also present several interesting examples showing a negative answer to some questions about these subgroups.
##### MSC:
 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, $$\pi$$-length, ranks 20D30 Series and lattices of subgroups 20F16 Solvable groups, supersolvable groups
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