Dimension subgroups, nilpotency indices, and the number of generators of ideals in p-group algebras

Aner Shalev

doi:10.1016/0021-8693(90)90228-G

Dimension subgroups, nilpotency indices, and the number of generators of ideals in p-group algebras

Aner Shalev^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

29 Scopus citations

Abstract

Various problems in modular p-group algebras are solved through extensive study of dimension subgroups. As an application it is shown that, if G is an infinite res-P group (p > 2) and K is a field of characteristic p, then the least upper bound on the numbers of generators of ideals in KG equals the minimal index of a cyclic Subgroup of G.

Original language	English
Pages (from-to)	412-438
Number of pages	27
Journal	Journal of Algebra
Volume	129
Issue number	2
DOIs	https://doi.org/10.1016/0021-8693(90)90228-G
State	Published - Mar 1990

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abstract = "Various problems in modular p-group algebras are solved through extensive study of dimension subgroups. As an application it is shown that, if G is an infinite res-P group (p > 2) and K is a field of characteristic p, then the least upper bound on the numbers of generators of ideals in KG equals the minimal index of a cyclic Subgroup of G.",

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Dimension subgroups, nilpotency indices, and the number of generators of ideals in p-group algebras

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