Integral Group Ring of Rudvalis Simple Group
نویسندگان
چکیده
Using the Luthar–Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Rudvalis sporadic simple group Ru. As a consequence, for this group we confirm Kimmerle’s conjecture on prime graphs.
منابع مشابه
3 N ov 2 00 8 Moonshine for Rudvalis ’ s sporadic group II ∗
In Part I we introduced the notion of enhanced vertex operator superalgebra, and constructed an example which is self-dual, has rank 28, and whose full symmetry group is a seven-fold cover of the sporadic simple group of Rudvalis. In this article we construct a second enhanced vertex operator superalgebra whose full automorphism group is a cyclic cover of the Rudvalis group. This new example is...
متن کاملar X iv : m at h / 06 11 35 5 v 1 [ m at h . R T ] 1 3 N ov 2 00 6 Moonshine for Rudvalis ’ s sporadic group II ∗
In Part I we introduced the notion of enhanced vertex operator superalgebra, and constructed an example which is self-dual, has rank 28, and whose full symmetry group is a seven-fold cover of the sporadic simple group of Rudvalis. In this article we construct a second enhanced vertex operator superalgebra whose full automorphism group is a cyclic cover of the Rudvalis group. This new example is...
متن کاملar X iv : m at h / 06 09 44 9 v 1 [ m at h . R T ] 1 5 Se p 20 06 Moonshine for Rudvalis ’ s sporadic group I ∗
We introduce the notion of vertex operator superalgebra with enhanced conformal structure, which is a refinement of the notion of vertex operator superalgebra. We exhibit several examples, including a particular one which is self-dual, and whose full symmetry group is a direct product of a cyclic group of order seven with the sporadic simple group of Rudvalis. We thus obtain an analogue of Mons...
متن کامل3 N ov 2 00 8 Moonshine for Rudvalis ’ s sporadic group I ∗
We introduce the notion of vertex operator superalgebra with enhanced conformal structure, which is a refinement of the notion of vertex operator superalgebra. We exhibit several examples, including a particular one which is self-dual, and whose full symmetry group is a direct product of a cyclic group of order seven with the sporadic simple group of Rudvalis. We thus obtain an analogue of Mons...
متن کاملThe 3-modular Characters of the Rudvalis Sporadic Simple Group and Its Covering Group
The decomposition numbers of the Rudvalis sporadic simple group and of its double covering group modulo 3 are completely determined. The results were obtained using the computer algebra system MOC developed by Jansen, Lux, Parker, and the author, but the proofs are given in conventional form and can be verified by hand with the ordinary character table.
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