Let (a1a2a3a4) and (a5a6) be disjoint cycles in S10. Show that there isno element x in S10 such that x2 = (a1a2a3a4)(a5a6).

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.1: Finite Permutation Groups
Problem 31E: Exercises Let f and g be disjoint cycles in Sn. Prove that fg=gf.
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Let (a1a2a3a4) and (a5a6) be disjoint cycles in S10. Show that there is
no element x in S10 such that x2 = (a1a2a3a4)(a5a6).

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