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Jan 14, 2015 at 21:15 comment added Geoff Robinson Yes, that is certainly true.
Jan 14, 2015 at 20:58 comment added Ofir Gorodetsky Thanks! A good answer, and using the normal p-complement I was able to solve my 2nd question (when $G(p)$ is a non-trivial subgroup, it is the subgroup generated by $p$'th powers).
Jan 14, 2015 at 20:41 vote accept Ofir Gorodetsky
Jan 12, 2015 at 8:15 history edited Geoff Robinson CC BY-SA 3.0
corrected typos, spacing
Jan 11, 2015 at 23:32 history edited Geoff Robinson CC BY-SA 3.0
clarified
Jan 11, 2015 at 23:10 history edited Geoff Robinson CC BY-SA 3.0
added explanation
Jan 11, 2015 at 21:09 history answered Geoff Robinson CC BY-SA 3.0