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A question of fully invariant subgroup

  1. Sep 4, 2008 #1
    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 ?
     
  2. jcsd
  3. Sep 5, 2008 #2

    tiny-tim

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    Welcome to PF!

    Hi rulin ! Welcome to PF! :smile:

    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? :wink:
     
  4. Sep 5, 2008 #3
    Maybe i don't know the order of the subgroup generated by P and Q, but this group satisfied above condition must be nilpotent.
     
  5. Sep 7, 2008 #4

    morphism

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    Well that doesn't say much, because any finite p-group is nilpotent.

    To be honest, I don't understand the relevance of tiny-tim's hint.
     
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