Multiplicative Jordan decomposition in group rings and p-groups with all noncyclic subgroups normal

Chia Hsin Liu

doi:10.1016/j.jalgebra.2012.07.010

Multiplicative Jordan decomposition in group rings and p-groups with all noncyclic subgroups normal

Chia Hsin Liu^*

^*Corresponding author for this work

Department of Mathematics

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

4 Citations (Scopus)

Abstract

Let p be a prime and let G be a finite p-group. We show that if the integral group ring Z[G] satisfies the multiplicative Jordan decomposition property, then every noncyclic subgroup of G is normal. This is used to simplify the work of Hales, Passi and Wilson on the classification of integral group rings of finite 2-groups with the multiplicative Jordan decomposition property.

Original language	English
Pages (from-to)	300-313
Number of pages	14
Journal	Journal of Algebra
Volume	371
DOIs	https://doi.org/10.1016/j.jalgebra.2012.07.010
Publication status	Published - 2012

Keywords

2-Group
Integral group rings
Jordan decomposition
Nilpotent element
Noncyclic subgroup
P-Group
Semisimple element
Unit group

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2012.07.010

Cite this

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title = "Multiplicative Jordan decomposition in group rings and p-groups with all noncyclic subgroups normal",

abstract = "Let p be a prime and let G be a finite p-group. We show that if the integral group ring Z[G] satisfies the multiplicative Jordan decomposition property, then every noncyclic subgroup of G is normal. This is used to simplify the work of Hales, Passi and Wilson on the classification of integral group rings of finite 2-groups with the multiplicative Jordan decomposition property.",

keywords = "2-Group, Integral group rings, Jordan decomposition, Nilpotent element, Noncyclic subgroup, P-Group, Semisimple element, Unit group",

author = "Liu, {Chia Hsin}",

year = "2012",

doi = "10.1016/j.jalgebra.2012.07.010",

language = "English",

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journal = "Journal of Algebra",

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AU - Liu, Chia Hsin

PY - 2012

Y1 - 2012

N2 - Let p be a prime and let G be a finite p-group. We show that if the integral group ring Z[G] satisfies the multiplicative Jordan decomposition property, then every noncyclic subgroup of G is normal. This is used to simplify the work of Hales, Passi and Wilson on the classification of integral group rings of finite 2-groups with the multiplicative Jordan decomposition property.

AB - Let p be a prime and let G be a finite p-group. We show that if the integral group ring Z[G] satisfies the multiplicative Jordan decomposition property, then every noncyclic subgroup of G is normal. This is used to simplify the work of Hales, Passi and Wilson on the classification of integral group rings of finite 2-groups with the multiplicative Jordan decomposition property.

KW - 2-Group

KW - Integral group rings

KW - Jordan decomposition

KW - Nilpotent element

KW - Noncyclic subgroup

KW - P-Group

KW - Semisimple element

KW - Unit group

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DO - 10.1016/j.jalgebra.2012.07.010

M3 - Article

AN - SCOPUS:84865568551

SN - 0021-8693

VL - 371

SP - 300

EP - 313

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Multiplicative Jordan decomposition in group rings and p-groups with all noncyclic subgroups normal

Abstract

Keywords

ASJC Scopus subject areas

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