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Zassenhaus conjecture for \(A_6\). (English) Zbl 1149.16027

The well-known Zassenhaus conjecture for the integral group ring of a finite group is studied, namely, that a torsion normalized unit is conjugate to some group element in the rational group algebra. This problem is still open, and few non-solvable groups are known to satisfy the conjecture. Recent papers, for instance by V. Bovdi, A. Konovalov, [Lond. Math. Soc. Lect. Note Ser. 339, 237-245 (2007; Zbl 1120.16025)], and V. A. Bovdi, A. B. Konovalov, S. Siciliano, [Rend. Circ. Mat. Palermo (2) 56, No. 1, 125-136 (2007; Zbl 1125.16020)], and the present paper use the method due to I. S. Luthar, I. B. S. Passi, [Proc. Indian Acad. Sci., Math. Sci. 99, No. 1, 1-5 (1989; Zbl 0678.16008)], for verification of the conjecture for particular simple groups. In this paper the author establishes the conjecture for the alternating group of degree 6.

MSC:

16U60 Units, groups of units (associative rings and algebras)
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
16S34 Group rings
20C30 Representations of finite symmetric groups

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References:

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