Multiplicative Jordan Decomposition in Group Rings of 3-Groups, II

Chia Hsin Liu; D. S. Passman

doi:10.1080/00927872.2013.766828

Multiplicative Jordan Decomposition in Group Rings of 3-Groups, II

Chia Hsin Liu^*, D. S. Passman

^*Corresponding author for this work

Department of Mathematics

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

3 Citations (Scopus)

Abstract

In this paper, we complete the classification of those finite 3-groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ℤ[G] satisfies the multiplicative Jordan decomposition (1) MJD. In the nonabelian case, we show that ℤ[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 3³ = 27.

Original language	English
Pages (from-to)	2633-2639
Number of pages	7
Journal	Communications in Algebra
Volume	42
Issue number	6
DOIs	https://doi.org/10.1080/00927872.2013.766828
Publication status	Published - 2014 Jun

Keywords

3-group
Integral group ring
Multiplicative Jordan decomposition

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2013.766828

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title = "Multiplicative Jordan Decomposition in Group Rings of 3-Groups, II",

abstract = "In this paper, we complete the classification of those finite 3-groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ℤ[G] satisfies the multiplicative Jordan decomposition (1) MJD. In the nonabelian case, we show that ℤ[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 33 = 27.",

keywords = "3-group, Integral group ring, Multiplicative Jordan decomposition",

author = "Liu, {Chia Hsin} and Passman, {D. S.}",

note = "Funding Information: The first author{\textquoteright}s research was supported in part by an NSC grant. The second author{\textquoteright}s research was supported in part by an NSA grant.",

year = "2014",

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doi = "10.1080/00927872.2013.766828",

language = "English",

volume = "42",

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journal = "Communications in Algebra",

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TY - JOUR

T1 - Multiplicative Jordan Decomposition in Group Rings of 3-Groups, II

AU - Liu, Chia Hsin

AU - Passman, D. S.

N1 - Funding Information: The first author’s research was supported in part by an NSC grant. The second author’s research was supported in part by an NSA grant.

PY - 2014/6

Y1 - 2014/6

N2 - In this paper, we complete the classification of those finite 3-groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ℤ[G] satisfies the multiplicative Jordan decomposition (1) MJD. In the nonabelian case, we show that ℤ[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 33 = 27.

AB - In this paper, we complete the classification of those finite 3-groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ℤ[G] satisfies the multiplicative Jordan decomposition (1) MJD. In the nonabelian case, we show that ℤ[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 33 = 27.

KW - 3-group

KW - Integral group ring

KW - Multiplicative Jordan decomposition

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EP - 2639

JO - Communications in Algebra

JF - Communications in Algebra

IS - 6

ER -

Multiplicative Jordan Decomposition in Group Rings of 3-Groups, II

Abstract

Keywords

ASJC Scopus subject areas

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