Geodesic
A note on a class of factorized $p$-groups
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 993-996
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In this note we study finite $p$-groups $G=AB$ admitting a factorization by an Abelian subgroup $A$ and a subgroup $B$. As a consequence of our results we prove that if $B$ contains an Abelian subgroup of index $p^{n-1}$ then $G$ has derived length at most $2n$.
In this note we study finite $p$-groups $G=AB$ admitting a factorization by an Abelian subgroup $A$ and a subgroup $B$. As a consequence of our results we prove that if $B$ contains an Abelian subgroup of index $p^{n-1}$ then $G$ has derived length at most $2n$.
Classification : 20D15, 20D40
Keywords: factorizable groups; products of subgroups; $p$-groups 
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Jabara, Enrico. A note on a class of factorized $p$-groups. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 993-996. http://geodesic.mathdoc.fr/item/CMJ_2005_55_4_a14/

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