On the prime graph question for integral group rings of Conway simple groups
نویسندگان
چکیده
منابع مشابه
Torsion Units in Integral Group Rings of Conway Simple Groups
Using the Luthar–Passi method, we investigate the possible orders and partial augmentations of torsion units of the normalized unit group of integral group rings of Conway simple groups Co1, Co2 and Co3. Let U(ZG) be the unit group of the integral group ring ZG of a finite group G, and V (ZG) be its normalized unit group
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Vasil'ev posed Problem 16.26 in [The Kourovka Notebook: Unsolved Problems in Group Theory, 16th ed.,Sobolev Inst. Math., Novosibirsk (2006).] as follows:Does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? Conjecture: $k = 5$.In [Zvezdina, On nonabelian simple groups having the same prime graph a...
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Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko simple groups. As a consequence, for the Janko groups J1, J2 and J3 we confirm Kimmerle’s conjecture on prime graphs.
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2019
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2019.02.005