СyclicNone of theseNon abelianO Non cyclicWhich of the followingct? *None of theseO U(14) is isomorphic to S3O U(14) is isomorphic to U(7)O U(14) is isomorphic to U(12)The number of elements in A6 is36720Об

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Answered: Which of the following is correct? *…

Which of the following is correct? * None of these U(14) is isomorphic to S3 O U(14) is isomorphic to U(7) O U(14) is isomorphic to U(12)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 19E: 19. a. Show that is isomorphic to , where the group operation in each of , and is addition. ...

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In Example 3, the group S(A) is nonabelian where A={ 1,2,3 }. Exhibit a set A such that S(A) is abelian. Example 3. We shall take A={ 1,2,3 } and obtain an explicit example of S(A). In order to define an element f of S(A), we need to specify f(1), f(2), and f(3). There are three possible choices for f(1). Since f is to be bijective, there are two choices for f(2) after f(1) has been designated, and then only once choice for f(3). Hence there are 3!=321 different mappings f in S(A).
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