1.your answers by either writing a sentence or two or by providing a counterexam-ple.Determine if the following statements are true or false and justify(a) If a group G acts on a set S, every element of S is fixed by the identity ofG.(b) Every group of order 42 has a normal subgroup of order 8.(c) Q x Q is a cyclic group.(d) It is obvious from every Cayley graph of a group G whether or not G iscyclic.(e) Z/15Z x Z/14Z is isomorphic to Z/21Z x Z/10Z.

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Answered: O If a group G acts on a set S, every…

O If a group G acts on a set S, every element of S is fixed by the identity of G. O Every group of order 42 has a normal subgroup of order 8. Qx Q is a cyclic group.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 10E: Exercises 10. Find an isomorphism from the multiplicative group to the group with multiplication...

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