Permutable implies ascendant

Statement
Any permutable subgroup of a group is an ascendant subgroup.

Similar facts

 * Permutable implies subnormal in finite
 * Permutable implies locally subnormal

Opposite facts

 * Permutable not implies subnormal
 * There exist permutable subgroups of arbitrarily large subnormal depth

Facts used

 * 1) uses::Permutable subgroup is normalized by any trivially intersecting infinite cyclic group