Bovdi, V. A.; Konovalov, A. B.; Linton, S. Torsion units in integral group ring of the Mathieu simple group \(M_{22}\). (English) Zbl 1225.16017 LMS J. Comput. Math. 11, 28-39 (2008). Summary: We investigate the possible character values of torsion units of the normalized unit group of the integral group ring of the Mathieu sporadic group \(M_{22}\). We confirm the Kimmerle conjecture on prime graphs for this group and specify the partial augmentations for possible counterexamples to the stronger Zassenhaus conjecture. Cited in 1 ReviewCited in 13 Documents 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 20D08 Simple groups: sporadic groups Keywords:Zassenhaus conjecture; prime graphs; torsion units; partial augmentations; integral group rings; Kimmerle conjecture; normalized unit groups; Mathieu group \(M_{22}\) Software:GAP; LAGUNA PDF BibTeX XML Cite \textit{V. A. Bovdi} et al., LMS J. Comput. Math. 11, 28--39 (2008; Zbl 1225.16017) Full Text: DOI arXiv OpenURL References: [1] DOI: 10.1016/0022-314X(87)90037-0 · Zbl 0611.16007 [2] DOI: 10.1007/BF02948947 · Zbl 0019.25105 [3] DOI: 10.1007/BF02874643 · Zbl 0678.16008 [4] Bovdi, Gomm. Algebra [5] Bovdi, Groups St. Andrews 2005 339 pp 237– (2007) [6] Bovdi, Publ. Math. Debrecen 65 pp 291– (2004) [7] Bovdi, J. Group Theory [8] Bleher, LMS J. Comput. Math. 3 pp 274– (2000) · Zbl 0960.20004 [9] Berman, Ukrain. Mat. Ž. 7 pp 253– (1955) [10] Artamonov, Algebra. Topology. Geometry pp 3– (1989) [11] Kimmerle, Groups, rings and algebras pp 215– (2006) [12] Jansen, An Atlas of Brauer Characters 11 (1995) [13] Höfert, Groups, rings and group rings pp 243– (2006) [14] Hertweck, Proc. Edinb. Math. Soc. [15] Hertweck, Comm. Algebra [16] Hertweck, Algebra Colloq. 13 pp 329– (2006) · Zbl 1097.16009 [17] Conway, Atlas of Finite Groups. Maximal subgroups and ordinary characters for simple groups. (1985) · Zbl 0568.20001 [18] Cohn, Canad. J. Math. 17 pp 583– (1965) · Zbl 0132.27404 [19] DOI: 10.1007/BF03031434 · Zbl 1125.16020 [20] Zassenhaus, Studies in mathematics (in honor of A. Almeida Costa) pp 119– (1974) · Zbl 0302.12006 [21] DOI: 10.1080/00927879108824263 · Zbl 0729.16021 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.