On units of group algebras of 2-groups of maximal class

Zs Balogh; A. Bovdi

doi:10.1081/AGB-120039288

On units of group algebras of 2-groups of maximal class

Zs Balogh, A. Bovdi

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

13 Citations (Scopus)

Abstract

We determine the number of elements of order two in the group of normalized units V(IF₂G) of the group algebra IF₂G of a 2-group of maximal class over the field IF₂ of two elements. As a consequence for the 2-groups G and H of maximal class we have that V(IF₂G) and V(IF₂H) are isomorphic if and only if G and H are isomorphic.

Original language	English
Pages (from-to)	3227-3245
Number of pages	19
Journal	Communications in Algebra
Volume	32
Issue number	8
DOIs	https://doi.org/10.1081/AGB-120039288
Publication status	Published - 2004
Externally published	Yes

Keywords

Element of order two
Group algebra
Group of units
Isomorphism

ASJC Scopus subject areas

Algebra and Number Theory

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10.1081/AGB-120039288

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abstract = "We determine the number of elements of order two in the group of normalized units V(IF2G) of the group algebra IF2G of a 2-group of maximal class over the field IF2 of two elements. As a consequence for the 2-groups G and H of maximal class we have that V(IF2G) and V(IF2H) are isomorphic if and only if G and H are isomorphic.",

keywords = "Element of order two, Group algebra, Group of units, Isomorphism",

author = "Zs Balogh and A. Bovdi",

note = "Funding Information: The research was supported by OTKA, grants No. T037202 and No. T043034.",

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AU - Bovdi, A.

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PY - 2004

Y1 - 2004

N2 - We determine the number of elements of order two in the group of normalized units V(IF2G) of the group algebra IF2G of a 2-group of maximal class over the field IF2 of two elements. As a consequence for the 2-groups G and H of maximal class we have that V(IF2G) and V(IF2H) are isomorphic if and only if G and H are isomorphic.

AB - We determine the number of elements of order two in the group of normalized units V(IF2G) of the group algebra IF2G of a 2-group of maximal class over the field IF2 of two elements. As a consequence for the 2-groups G and H of maximal class we have that V(IF2G) and V(IF2H) are isomorphic if and only if G and H are isomorphic.

KW - Element of order two

KW - Group algebra

KW - Group of units

KW - Isomorphism

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JF - Communications in Algebra

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ER -

On units of group algebras of 2-groups of maximal class

Abstract

Keywords

ASJC Scopus subject areas

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