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Paper IPM / M / 8006  


Abstract:  
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 L_{n}(2) with n ≥ 3. First, for all n ≥ 3 we
establish that every finite group G with ω(G)=ω(L)
has a unique nonabelian 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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