Timeline for Questions about some finite p-groups of coclass 2

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May 7, 2014 at 15:19	history	edited	Lee Mosher		edited tags
May 7, 2014 at 10:26	comment	added	Marco Ruscitti		@YassineGuerboussa thank you for your answers. About the Frattini subgroup, the answer is very easy, i should not ask for. Instead i've no answers about $\Omega_{1}(Z_{2}(G))$.
May 7, 2014 at 10:16	history	edited	Marco Ruscitti	CC BY-SA 3.0	added 1 character in body
May 6, 2014 at 14:27	comment	added	Yassine Guerboussa		Now I suppose that you mean $\Phi(G)=Z_{n-3}(G)$ in your second question. I think yes, $G/Z_{n-3}$ has order $p^2$ and it is not cyclic, thus it contains $\Phi(G)$. Since $G$ is 2-generated, it follows that $\Phi(G)=Z_{n-3}(G)$.
May 6, 2014 at 14:18	comment	added	Yassine Guerboussa		The conditions 4, 6, 7, can be deduced from 1 and 5. Also if $G$ is not regular then $cl(G) \geq p$. I suppose that $n$ is defined by $p^n=\|G\|$, if so then $G$ has class $n-2$; however if $\Phi(G)=Z_{n-4}$, then $Z_{n-3}(G)=G$ which means that $G$ has class $n-3$. I wish that you edit your question with this remarks in mind.
May 6, 2014 at 9:48	history	asked	Marco Ruscitti	CC BY-SA 3.0