Abstract: Let Gr be the relatively free group of rank r in the variety generated by a finite group H. In this paper we determine the minimum positive integer t(r) for which Gr is embedded in the direct product of t(r) copies of H when H is a minimal non-abelian group or a dihedral group Dn (n odd). Moreover the finite nilpotent groups of class c are characterized as those finite groups for which t(r) is bounded from above by a polynomial of degree c.
The Birkhoff-Neumann embedding of relatively free groups / R. Brandl; G. Corsi Tani; L. Serena. - In: RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA. - ISSN 0041-8994. - STAMPA. - 115:(2006), pp. 85-97.
The Birkhoff-Neumann embedding of relatively free groups
SERENA, LUIGI
2006
Abstract
Abstract: Let Gr be the relatively free group of rank r in the variety generated by a finite group H. In this paper we determine the minimum positive integer t(r) for which Gr is embedded in the direct product of t(r) copies of H when H is a minimal non-abelian group or a dihedral group Dn (n odd). Moreover the finite nilpotent groups of class c are characterized as those finite groups for which t(r) is bounded from above by a polynomial of degree c.
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