a) In G = (Z54,) find [G:H] for H=< 24 >. b) Let |G|=8 and G is not cyclic. Show that g4 = e for every g E G.

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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3.
a) In G = (Z54,) find [G:H] for H=< 24 >.
b) Let |G|=8 and G is not cyclic. Show that g
4
= e for every gEG.
Transcribed Image Text:3. a) In G = (Z54,) find [G:H] for H=< 24 >. b) Let |G|=8 and G is not cyclic. Show that g 4 = e for every gEG.
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