3,312 research outputs found

    On the isomorphism problem for unit groups of modular group algebras

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    Using the computational algebra system GAP (http://www.gap-system.org) and the GAP package LAGUNA (http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm), we checked that all 2-groups of order not greater than 32 are determined by normalized unit groups of their modular group algebras over the field of two elements.Comment: 6 pages, accepted in Acta Sci. Math. (Szeged

    Kimmerle conjecture for the Held and O'Nan sporadic simple groups

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    Using the Luthar--Passi method, we investigate the Zassenhaus and Kimmerle conjectures for normalized unit groups of integral group rings of the Held and O'Nan sporadic simple groups. We confirm the Kimmerle conjecture for the Held simple group and also derive for both groups some extra information relevant to the classical Zassenhaus conjecture.Comment: 9 page

    Integral group ring of the first Mathieu simple group

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    We investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Mathieu group M11. As a consequence, for this group we confirm the conjecture by Kimmerle about prime graphs

    Integral group ring of the McLaughlin simple group

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    We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the McLaughlin sporadic group McL. As a consequence, we confirm for this group the Kimmerle’s conjecture on prime graphs

    Kimmerle conjecture for the Held and O'Nan sporadic simple groups

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    Using the Luthar--Passi method, we investigate the Zassenhaus and Kimmerle conjectures for normalized unit groups of integral group rings of the Held and O'Nan sporadic simple groups. We confirm the Kimmerle conjecture for the Held simple group and also derive for both groups some extra information relevant to the classical Zassenhaus conjecture

    Torsion units in integral group rings of Janko simple groups

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    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 J1J_1, J2J_2 and J3J_3 is the same as that of the normalized unit group of their respective integral group ring.Comment: 23 pages, to appear in Math.Comp
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