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Each finite $p$-group $H$ may be embedded in the Frattini subgroup of an appropriate $p$-group $G$ (for example, $G=H \wr C_p$; here $d(G)\le d(H)+1$. If $G$ is such, then its Frattini subgroup $\Phi(G)$ contains a subgroup which is isomorphic with $H$.)

Problem. Is it true that one can choose $G$ so that $d(G)=2$?

Yakov

Each finite $p$-group $H$ may be embedded in the Frattini subgroup of an appropriate $p$-group $G$ (for example, $G=H \wr C_p$; here $d(G)\le d(H)+1$. Then for this $G$, the Frattini subgroup $\Phi(G)$ contains a subgroup which is isomorphic to $H$.)

Problem. Is it true that one can choose $G$ so that $d(G)=2$?

Yakov

Each finite $p$-group $H$ may be embedded in the Frattini subgroup of an appropriate $p$-group $G$ (for example, $G=H \wr C_p$; here $d(G)\le d(H)+1$.)

Problem. Is it true that one can choose $G$ so that $d(G)=2$?

Yakov

Each finite $p$-group $H$ may be embedded in the Frattini subgroup of an appropriate $p$-group $G$ (for example, $G=H \wr C_p$; here $d(G)\le d(H)+1$. If $G$ is such, then its Frattini subgroup $\Phi(G)$ contains a subgroup which is isomorphic with $H$.)

Problem. Is it true that one can choose $G$ so that $d(G)=2$?

Yakov

Each finite p-group H may be embedded in the Frattini subgroup of an appropriate p-group G (for example, G=H wr C_p; here d(G)\le d(H)+1.)

Problem. Is it true that one can choose G so that d(G)=2?

Yakov

Each finite $p$-group $H$ may be embedded in the Frattini subgroup of an appropriate $p$-group $G$ (for example, $G=H \wr C_p$; here $d(G)\le d(H)+1$.)

Problem. Is it true that one can choose $G$ so that $d(G)=2$?

Yakov