The spectrum of a periodic group G is the set ω(G) of its element orders. The objective of the present paper is to consider the simple group L 3 (4) which is isomorphic to M 21 . Theorem. If ω(G)={1,2,3,4,5,7}=ω(L 3 (4)), then G is isomorphic to L 3 (4). For finite groups G, the result was proved by W. Shi
Recognizing L (3)(4) by the Set of Element Orders in the Class of All Groups
JABARA, Enrico;
2015-01-01
Abstract
The spectrum of a periodic group G is the set ω(G) of its element orders. The objective of the present paper is to consider the simple group L 3 (4) which is isomorphic to M 21 . Theorem. If ω(G)={1,2,3,4,5,7}=ω(L 3 (4)), then G is isomorphic to L 3 (4). For finite groups G, the result was proved by W. Shi
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