The spectrum omega(G) of a finite group G is the set of orders of elements of G. We present a polynomial-time algorithm that, given a finite set M of positive integers, outputs either an empty set or a finite simple g...
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The spectrum omega(G) of a finite group G is the set of orders of elements of G. We present a polynomial-time algorithm that, given a finite set M of positive integers, outputs either an empty set or a finite simple group G. In the former case, there is no finite simple group H with M = omega(H), while in the latter case, M subset of omega(G) and M not equal omega(H) for all finite simple groups H with omega(H) not equal omega(G). (C) 2019 Elsevier Inc. All rights reserved.
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