Group algebras with unit group of class p

Zsolt Balogh; Adalbert Bovdi

doi:10.5486/pmd.2004.3239

Group algebras with unit group of class p

Zsolt Balogh, Adalbert Bovdi

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Let V(script F sign_pG) be the group of normalized units of the group algebra script F sign_pG of a finite nonabelian p-group G over the field script F sign_p of p elements. Our goal is to investigate the power structure of V(script F sign_pG), when it has nilpotency class p. As a consequence, we have proved that if G and H are p-groups with cyclic Frattini subgroups and p > 2, then V(script F sign_pG) is isomorphic to V(script F sign_pH) if and only if G and H are isomorphic.

Original language	English
Pages (from-to)	261-268
Number of pages	8
Journal	Publicationes Mathematicae Debrecen
Volume	65
Issue number	3-4
DOIs	https://doi.org/10.5486/pmd.2004.3239
Publication status	Published - 2004
Externally published	Yes

Keywords

Group algebra
Group of units
Isomorphism problem

ASJC Scopus subject areas

General Mathematics

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10.5486/pmd.2004.3239

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AU - Balogh, Zsolt

AU - Bovdi, Adalbert

PY - 2004

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N2 - Let V(script F signpG) be the group of normalized units of the group algebra script F signpG of a finite nonabelian p-group G over the field script F signp of p elements. Our goal is to investigate the power structure of V(script F signpG), when it has nilpotency class p. As a consequence, we have proved that if G and H are p-groups with cyclic Frattini subgroups and p > 2, then V(script F signpG) is isomorphic to V(script F signpH) if and only if G and H are isomorphic.

AB - Let V(script F signpG) be the group of normalized units of the group algebra script F signpG of a finite nonabelian p-group G over the field script F signp of p elements. Our goal is to investigate the power structure of V(script F signpG), when it has nilpotency class p. As a consequence, we have proved that if G and H are p-groups with cyclic Frattini subgroups and p > 2, then V(script F signpG) is isomorphic to V(script F signpH) if and only if G and H are isomorphic.

KW - Group algebra

KW - Group of units

KW - Isomorphism problem

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JO - Publicationes Mathematicae Debrecen

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ER -

Group algebras with unit group of class p

Abstract

Keywords

ASJC Scopus subject areas

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