Groups of exponent 60 with prescribed orders of elements

We prove that a group which contains elements of orders 1, 2, 3, 4, 5 and does not contain elements of any other order is locally finite and isomorphic either to an alternating group of degree 6 or to an extension of a nontrivial elementary Abelian 2-group by an alternating group of degree 5. This article was written during my visit to the University of Manitoba, Canada, and supported by RFFR grant No. 99-01-00550. Translated fromAlgebra i Logika, Vol. 39, No. 3, pp. 329–346, May–June, 2000.