we prove that the class of profinite groups $g$ that have a factorization $g=ab$ with $a$ and $b$ abelian closed subgroups, is closed under taking strict projective limits. this is a generalization of a recent result by k.h.~hofmann and f.g.~russo. as an application we reprove their generalization of iwasawa's structure theorem for quasihamiltonian pro-$p$ groups.

Let F ^ \hat {F} </mml:...

Among the six classes of pro-2-groups of finite and fixed co-classes and trivial Schur Multiplicator which studied by Abdolzadeh and Eick in 2009, there are two classes $$S_5=langle a,bmid [b,a^2]=1, a^2=[b,a]^2, (b^2)^{[b,a]}b^2=1rangle$$ and $$S_6=langle a,t,bmid a^2=b^2,[b,a]^2=1, t^a=t^{-1}[b,a], b^t=abarangle$$that have been conjectured to have deficiency zero presentations. In this paper ...

we prove that the class of profinite groups $g$ that have a factorization $g=ab$‎ ‎with $a$ and $b$ abelian closed subgroups‎, ‎is closed under taking inverse limits‎ ‎of surjective inverse systems‎. ‎this is a generalization of a recent result by k. h. hofmann and f. g. russo‎. ‎as an application we reprove their generalization of iwasawa&apos;s structure theorem for‎ ‎quasihamiltonian pro-$p$...

Let $p$ be a prime. A pro-$p$ group $G$ is said to 1-smooth if it can endowed with homomorphism of groups $G\to1+p\mathbb{Z}_p$ satisfying formal version Hilbert 90. By Kummer theory, maximal Galois fields containing root 1 order $p$, together the cyclotomic character, are 1-smooth. We prove that finitely generated $p$-adic analytic if, and only occurs as field $p$. This gives positive answer D...

among the six classes of pro-2-groups of finite and fixed co-classes and trivial schur multiplicator which studied by abdolzadeh and eick in 2009, there are two classes $$s_5=langle a,bmid [b,a^2]=1, a^2=[b,a]^2, (b^2)^{[b,a]}b^2=1rangle$$ and $$s_6=langle a,t,bmid a^2=b^2,[b,a]^2=1, t^a=t^{-1}[b,a], b^t=abarangle$$that have been conjectured to have deficiency zero presentations. in this paper ...