Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

$p$-groups are locally nilpotent groups? How can we show it? I know that a finite $p$-group is nilpotent. If in general the answer is "no", then what about a FC $p$-group?

share|cite|improve this question
Tarski monsters are non-(locally nilpotent) p-groups. – Jack Schmidt Oct 12 '12 at 16:45
There are finitely generated p groups which are not nilpotent. – Mustafa Gokhan Benli Oct 12 '12 at 16:48
Thanks. Do You know something about $FC\space p$-groups? Are they locally nilpotent groups? – W4cc0 Oct 12 '12 at 16:48
up vote 0 down vote accepted

In periodic $FC$-groups Dietzmann's lemma forces $G$ to be locally nipotent.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.