On a Filtered Multiplicative Bases of Group Algebras II

Victor Bovdi

doi:10.1023/A:1025168211902

On a Filtered Multiplicative Bases of Group Algebras II

Victor Bovdi

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

11 Citations (Scopus)

Abstract

We give an explicit list of all p-groups G with a cyclic subgroup of index p², such that the group algebra KG over the field K of characteristic p has a filtered multiplicative K -basis. We also prove that such a K -basis does not exist for the group algebra KG, in the case when G is either a non-Abelian powerful p-group or a two generated p-group (p ≠ 2) with a central cyclic commutator subgroup. This paper is a continuation of the paper which appeared in Arch. Math. (Basel) 74 (2000), 217-285.

Original language	English
Pages (from-to)	353-368
Number of pages	16
Journal	Algebras and Representation Theory
Volume	6
Issue number	3
DOIs	https://doi.org/10.1023/A:1025168211902
Publication status	Published - Aug 2003
Externally published	Yes

Keywords

Filtered multiplicative basis
Finite-dimensional algebras
Group algebras

ASJC Scopus subject areas

General Mathematics

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10.1023/A:1025168211902

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author = "Victor Bovdi",

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N2 - We give an explicit list of all p-groups G with a cyclic subgroup of index p2, such that the group algebra KG over the field K of characteristic p has a filtered multiplicative K -basis. We also prove that such a K -basis does not exist for the group algebra KG, in the case when G is either a non-Abelian powerful p-group or a two generated p-group (p ≠ 2) with a central cyclic commutator subgroup. This paper is a continuation of the paper which appeared in Arch. Math. (Basel) 74 (2000), 217-285.

AB - We give an explicit list of all p-groups G with a cyclic subgroup of index p2, such that the group algebra KG over the field K of characteristic p has a filtered multiplicative K -basis. We also prove that such a K -basis does not exist for the group algebra KG, in the case when G is either a non-Abelian powerful p-group or a two generated p-group (p ≠ 2) with a central cyclic commutator subgroup. This paper is a continuation of the paper which appeared in Arch. Math. (Basel) 74 (2000), 217-285.

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KW - Finite-dimensional algebras

KW - Group algebras

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ER -

On a Filtered Multiplicative Bases of Group Algebras II

Abstract

Keywords

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