Abstract: | We prove that if the factor group H=G/N of a finite group G is isomorphic to a symmetric or alternating group of degree m,
where m≥5 and N≠1, then G has an element whose order is distinct from any element’s order in H.
Supported by RFFR grant No. 96-01-01893.
Translated fromAlgebra i Logika, Vol. 38, No. 3, pp. 296–315, May–June, 1999. |