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Paper   IPM / M / 7610
School of Mathematics
  Title:   Groups with the same orders of Sylow normalizers as the Janko groups
  Author(s): 
1.  Behr. Khosravi
2.  Behn. Khosravi
  Status:   Published
  Journal: J. Appl. Algebra Discrete Struct.
  Vol.:  3
  Year:  2005
  Pages:   23-31
  Supported by:  IPM
  Abstract:
In this paper, we prove that the Janko groups are uniquely determined by their orders of Sylow normalizers. Let$πn(G) = {(p,|NG(P)|)|pSylp(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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