## On inert subgroups of a group.(English)Zbl 1167.20319

Summary: A subgroup $$H$$ of a group $$G$$ is called inert if $$|H:H\cap H^g|$$ is finite for all $$g$$ in $$G$$. If every subgroup of $$G$$ is inert, then $$G$$ is said to be inertial. After giving an account of the basic properties of inert subgroups, we study the structure of inertial soluble groups. A classification is obtained for the groups which are finitely generated or have finite Abelian total rank.

### MSC:

 20E07 Subgroup theorems; subgroup growth 20F16 Solvable groups, supersolvable groups 20F05 Generators, relations, and presentations of groups
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### References:

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