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Torsion matrices over commutative integral group rings.

Gregory T. Lee, Sudarshan K. Sehgal (2000)

Publicacions Matemàtiques

Let ZA be the integral group ring of a finite abelian group A, and n a positive integer greater than 5. We provide conditions on n and A under which every torsion matrix U, with identity augmentation, in GLn(ZA) is conjugate in GLn(QA) to a diagonal matrix with group elements on the diagonal. When A is infinite, we show that under similar conditions, U has a group trace and is stably conjugate to such a diagonal matrix.

Torsion units for some almost simple groups

Joe Gildea (2016)

Czechoslovak Mathematical Journal

We investigate the Zassenhaus conjecture regarding rational conjugacy of torsion units in integral group rings for certain automorphism groups of simple groups. Recently, many new restrictions on partial augmentations for torsion units of integral group rings have improved the effectiveness of the Luther-Passi method for verifying the Zassenhaus conjecture for certain groups. We prove that the Zassenhaus conjecture is true for the automorphism group of the simple group PSL ( 2 , 11 ) . Additionally we prove that...

Torsion units in group rings.

Vikas Bist (1992)

Publicacions Matemàtiques

Let U(RG) be the unit group of the group ring RG. In this paper we study group rings RG whose support elements of every torsion unit are torsion, where R is either the ring of integers Z or a field K.

Totally inert groups

V. V. Belyaev, M. Kuzucuoğlu, E. Seçkin (1999)

Rendiconti del Seminario Matematico della Università di Padova

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