$p$-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?
Locally nilpotent groups
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abstract-algebra
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0Thanks. Do You know something about $FC\space p$-groups? Are they locally nilpotent groups? – 2012-10-12
1 Answers
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In periodic $FC$-groups Dietzmann's lemma forces $G$ to be locally nipotent.