On finite $p$-groups that are the product of a subgroup of class two and an abelian subgroup of order $p^3$

McCann, Brendan

doi:10.4171/RSMUP/136-1

On finite

p

-groups that are the product of a subgroup of class two and an abelian subgroup of order

p^{3}

McCann, Brendan ¹

¹ Waterford Institute of Technology, WATERFORD, IRELAND

Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 1-10.

Résumé

In this note it is shown that if $G = A B$ is a fi nite $p$ -group that is the product of an abelian subgroup $A$ of order $p^{3}$ and a subgroup $B$ of nilpotency class two, then $G$ can have derived length at most three.

DOI : 10.4171/RSMUP/136-1

Classification : 20
Mots clés : Products of groups, factorised groups, finite $p$-groups

Affiliations des auteurs :

McCann, Brendan ¹

¹ Waterford Institute of Technology, WATERFORD, IRELAND

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     title = {On finite $p$-groups that are the product of a subgroup of class two and an abelian subgroup of order $p^3$},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {1--10},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {136},
     year = {2016},
     doi = {10.4171/RSMUP/136-1},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/136-1/}
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McCann, Brendan. On finite $p$-groups that are the product of a subgroup of class two and an abelian subgroup of order $p^3$. Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 1-10. doi : 10.4171/RSMUP/136-1. http://www.numdam.org/articles/10.4171/RSMUP/136-1/

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