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Paper   IPM / M / 8006
School of Mathematics
  Title:   On recognition of the projective special linear groups over binary field
  Author(s):  A. R. Moghaddamfar (Joint with M. A. Grechkoseeva, M S. Lucido, V. D. Mazurov, and A. V. Vasil'ev)
  Status:   Published
  Journal: Siberian Electroic Mathematical Reports
  Vol.:  2
  Year:  2005
  Pages:   253-263
  Supported by:  IPM
The spectrum ω(G) of a finite group G is the set of element orders of G. Let L be the projective special linear group Ln(2) with n ≥ 3. First, for all n ≥ 3 we establish that every finite group G with ω(G)=ω(L) has a unique non-abelian composition factor and this factor is isomorphic to L. Second, for some special series of integers n we prove that L is recognizable by spectrum, i.e. every finite group G with ω(G)=ω(L) is isomorphic to L.

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