On the localization genus of a direct product of metacyclic groups

Peter J. Witbooi

Type: Article

Publication Date: 2009-01-01

Citations: 0

DOI: https://doi.org/10.1515/jgt.2009.017

Abstract

For groups H of the type G(n; u) × G(m; u) we determine the set χ(H) of all isomorphism classes of groups K with the property that K × ℤ ≅ H × ℤ. The set χ(H) carries a certain group structure which coincides with the Hilton–Mislin genus group structure when H is nilpotent. We compute the group χ(H).

Locations

Journal of Group Theory - View - PDF

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Works Cited by This (11)

Action	Title	Year	Authors
+	On the genus of a nilpotent group with finite commutator subgroup	1976	Peter Hilton Guido Mislin
+	The non-cancellation group of a direct power of a (finite cyclic)-by-cyclic group	2004	Peter J. Witbooi
+	Non-cancellation and Mislin genus of certain groups and H0-spaces	2002	Dirk Scevenels Peter J. Witbooi
+ PDF Chat	Calculating the genus of a direct product of certain nilpotent groups	1995	P. J. Hilton Dirk Scevenels
+	Generalizing the Hilton–Mislin Genus Group	2001	Peter J. Witbooi
+	A discrete homotopy theory for binary reflexive structures	2004	Benoît Larose Claude Tardif
+	The minimal relation modules of a finite Abelian group	1981	Peter Webb
+	Non-cancellation for groups with non-abelian torsion	2003	Peter J. Witbooi
+	Genus and cancellation	2000	Niamh OʼSullivan
+	Calculating the mislin genus for a certain family of nilpotent groups	1991	Carles Casacuberta Peter Hilton