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AbstractIn a finite group G, let πe(G){\pi_{e}(G)}be the set of orders of elements of G, let sk{s_{k}}denote the number of elements of order k in G, for each k∈πe(G){k\in\pi_{e}(G)}, and then let nse(G){\operatorname{nse}(G)}be the unordered set {sk:k∈πe(G)}{\{s_{k}:k\in\pi_{e}(G)\}}.In this paper, it is shown that if |G|=|L2(q)|{\lvert G\rvert=\lvert L_{2}(q)\rvert}and nse(G)=nse(L2(q)){\operatorname{nse}(G)=\operatorname{nse}(L_{2}(q))}for some prime-power q, then G is isomorphic to L2(q){L_{2}(q)}.
Groups Complexity Cryptology – de Gruyter
Published: Nov 1, 2018
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