Consider G=D(5) a dihedral group as a group ofpermutations shown belowsage: G=Dihedral Group(5)sage: list(G)[(), (1,5,4,3,2), (1,4,2,5,3), (1,3,5,2,4), (1,2,3,4,5),(2,5)(3,4), (1,5)(2,4), (1,4)(2,3), (1,3)(4,5), (1,2)(3,5)]a) Is {(),(1,3)(4,5} a subgroup of G?b)Is {(), (1,3)(4,5} a normal subgroup of G?

Answered: Consider G=D(5) a dihedral group as a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.4: Cosets Of A Subgroup

Problem 24E: Find two groups of order 6 that are not isomorphic.

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