# A question of fully invariant subgroup

## Main Question or Discussion Point

A subgroup H of a group G is fully invariant if t(H)<=H for every endomorphism t of G. Let G is finite p-group has a fully invariant subgroup of order d for every d dividing |G|. What is the structure of G ?

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A subgroup H of a group G is fully invariant if t(H)<=H for every endomorphism t of G. Let G is finite p-group has a fully invariant subgroup of order d for every d dividing |G|. What is the structure of G ?
Hi rulin ! Welcome to PF!

Hint: if p and q are different prime factors of |G|, and their fully invariant subgroups are P and Q, then what is the order of the subgroup generated by P and Q?

Maybe i don't know the order of the subgroup generated by P and Q, but this group satisfied above condition must be nilpotent.

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