# I A p-primary group G that is not divisible -- Show that <y> is pure in G.

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1. Feb 9, 2017

### STF92

Hi: Let G be a p-primary group that is not divisible. Assume there is x in G[p] that is divisible by pk but not by pk+1 and let x= pk y. Show that <y> is pure in G.

Let x \in G[p] such as described. I must prove that <y> intersection nG is a subset of n<y>. pk+1y= px =0. In case (n,p)=1, there is b in <y> such that y=nb and then sy= snb= n(sb) in n<y>. But when (n,p) not equal 1 I cannot find a way. Could you tell me how I should proceed?