Baer-Suzuki theorem for the π-radical
نویسندگان
چکیده
In the paper we prove (modulo classification of finite simple groups) an analogue famous Baer-Suzuki theorem for π-radical a group, where π is set primes.
منابع مشابه
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Suppose that G is a finite group and x ∈ G has prime order p ≥ 5. Then x is contained in the solvable radical of G, O∞(G), if (and only if) 〈x, xg〉 is solvable for all g ∈ G. If G is an almost simple group and x ∈ G has prime order p ≥ 5, then this implies that there exists g ∈ G such that 〈x, xg〉 is not solvable. In fact, this is also true when p = 3 with very few exceptions, which are describ...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2021
ISSN: ['1565-8511', '0021-2172']
DOI: https://doi.org/10.1007/s11856-021-2209-y