Abstract
Let G be a finite group. The set of all prime divisors of the order of G is called the prime spectrum of G and is denoted by π(G). A group G is called prime spectrum minimal if π(G) ≠ π(H) for any proper subgroup H of G. We prove that every prime spectrum minimal group all of whose nonabelian composition factors are isomorphic to the groups from the set {PSL 2(7), PSL 2(11), PSL 5(2)} is generated by two conjugate elements. Thus, we extend the corresponding result for finite groups with Hall maximal subgroups. Moreover, we study the normal structure of a finite prime spectrum minimal group with a nonabelian composition factor whose order is divisible by exactly three different primes.
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Original Russian Text © N.V.Maslova, 2015, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Vol. 21, No. 3.
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Maslova, N.V. On the finite prime spectrum minimal groups. Proc. Steklov Inst. Math. 295 (Suppl 1), 109–119 (2016). https://doi.org/10.1134/S0081543816090121
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DOI: https://doi.org/10.1134/S0081543816090121