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| Paper IPM / M / 7610 |
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| Abstract: | |||||
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In this paper, we prove that the Janko groups are
uniquely determined by their orders of Sylow normalizers. Let$πn(G) = {(p,|NG(P)|)|p ∈ Sylp(G), forall p ∈ π(G)}. Then we prove the following theorems:Theorem A. Let J be a Janko group. If G is a finitegroup such that _n(G)= _n(J), then G.\ Theorem B. Let J be a Janko group and p:=max{q - q(J)}. If G is a finite group such that J and G have the same order and - N_J(P) - = - N_G(P^) - , where P Syl_p(J) and P^ Syl_p(G), thenG
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