Torsion units in integral group rings of Janko simple groups

V. A. Bovdi; E. Jespers; A. B. Konovalov

doi:10.1090/S0025-5718-2010-02376-2

Torsion units in integral group rings of Janko simple groups

V. A. Bovdi
, E. Jespers
, A. B. Konovalov

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

20 Citations (Scopus)

Abstract

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko sporadic simple groups. As a consequence, we obtain that the Gruenberg-Kegel graph of the Janko groups J₁, J₂ and J₃ is the same as that of the normalized unit group of their respective integral group ring.

Original language	English
Pages (from-to)	593-615
Number of pages	23
Journal	Mathematics of Computation
Volume	80
Issue number	273
DOIs	https://doi.org/10.1090/S0025-5718-2010-02376-2
Publication status	Published - 2010
Externally published	Yes

Keywords

Integral group ring
Partial augmentation
Prime graph
Torsion unit
Zassenhaus conjecture

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/S0025-5718-2010-02376-2

Cite this

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title = "Torsion units in integral group rings of Janko simple groups",

abstract = "Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko sporadic simple groups. As a consequence, we obtain that the Gruenberg-Kegel graph of the Janko groups J1, J2 and J3 is the same as that of the normalized unit group of their respective integral group ring.",

keywords = "Integral group ring, Partial augmentation, Prime graph, Torsion unit, Zassenhaus conjecture",

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T1 - Torsion units in integral group rings of Janko simple groups

AU - Bovdi, V. A.

AU - Jespers, E.

AU - Konovalov, A. B.

PY - 2010

Y1 - 2010

N2 - Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko sporadic simple groups. As a consequence, we obtain that the Gruenberg-Kegel graph of the Janko groups J1, J2 and J3 is the same as that of the normalized unit group of their respective integral group ring.

AB - Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko sporadic simple groups. As a consequence, we obtain that the Gruenberg-Kegel graph of the Janko groups J1, J2 and J3 is the same as that of the normalized unit group of their respective integral group ring.

KW - Integral group ring

KW - Partial augmentation

KW - Prime graph

KW - Torsion unit

KW - Zassenhaus conjecture

UR - https://www.scopus.com/pages/publications/78649352865

UR - https://www.scopus.com/pages/publications/78649352865#tab=citedBy

U2 - 10.1090/S0025-5718-2010-02376-2

DO - 10.1090/S0025-5718-2010-02376-2

M3 - Article

AN - SCOPUS:78649352865

SN - 0025-5718

VL - 80

SP - 593

EP - 615

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 273

ER -

Torsion units in integral group rings of Janko simple groups

Abstract

Keywords

ASJC Scopus subject areas

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