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Torsion units in the integral group ring of the alternating group of degree 6. (English) Zbl 1161.16023

Motivated by a conjecture of H. Zassenhaus and a conjecture of W. Kimmerle, the author studies the orders and partial augmentations of torsion units in the integral group ring of the alternating group of degree \(6\). Some of the torsion units are shown to be rationally conjugate to an element of the base group, whereas for others it is proved that their partial augmentations are bounded by \(-2\) and \(2\).

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

Software:

LAGUNA
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References:

[1] Berman S. D., Ukrain Mat. Z. 7 pp 253– (1955)
[2] DOI: 10.1112/S1461157000000309 · Zbl 0960.20004
[3] Bovdi V., Publ. Math. Debrecen 65 pp 291– (2004)
[4] Bovdi V., Integral Group Rings of the First Simple Mathieu Group M 11 · Zbl 1120.16025
[5] Bovdi V., LAGUNA–Lie Algebras and Units of Group Algebras (2006) · Zbl 1120.16301
[6] DOI: 10.4153/CJM-1965-058-2 · Zbl 0132.27404
[7] DOI: 10.1080/00927879708825991 · Zbl 0881.16020
[8] Hertweck M., Algebra Colloquium 13 pp 328– (2006)
[9] Kimmerle I. W., On the Prime Graph of the Unit Group of Integral Group rings of Finite Groups, Groups, Rings and Algebras · Zbl 1126.20001
[10] DOI: 10.1007/BF02874643 · Zbl 0678.16008
[11] DOI: 10.1080/00927879108824263 · Zbl 0729.16021
[12] DOI: 10.1016/0022-314X(87)90037-0 · Zbl 0611.16007
[13] DOI: 10.2307/1971362 · Zbl 0633.20003
[14] DOI: 10.1515/crll.1991.415.175 · Zbl 0744.16019
[15] Zassenhaus H., Inst. Alta Cultura Lisbon 51 pp 119– (1974)
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