Plz answer all parts correctly asap 7. Define the setG =(a) It is a fact that G is a group.cos{[ ]|OER}sin 0sincosYou do not need to prove all of the requirements but showthere is an identity and show closure.(b) For n € Z+ prove that G contains an element of order n.(c) For ne Z+ prove that G contains a subgroup isomorphic to Zn by providing the isomor-phism and proving that it is an isomorphism.

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Define the set G= ={[ 0]|PER} cos sin 0 - sin cos (a) It is a fact that G is a group. You do not need to prove all of the requirements but show there is an identity and show closure. (b) For ne Z+ prove that G contains an element of order n. (c) For n € Z+ prove that G contains a subgroup isomorphic to Zn by providing the isomor- phism and proving that it is an isomorphism.

Define the set G= ={[ 0]|PER} cos sin 0 - sin cos (a) It is a fact that G is a group. You do not need to prove all of the requirements but show there is an identity and show closure. (b) For ne Z+ prove that G contains an element of order n. (c) For n € Z+ prove that G contains a subgroup isomorphic to Zn by providing the isomor- phism and proving that it is an isomorphism.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 32E: 32. Let be a fixed element of the group . According to Exercise 20 of section 3.5, the mapping ...

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