Q1/AI Prove that the mathematical system (s), where (o) is an usualcomposition map is a group?B/ Write the element of the group S, and prove that it is not abelian group?Q2/A/ Let G be a group and K, H be subgroups of G. Prove that H UK is asubgroup of G iff H CK or KCH?B/ Find the generated element of the following:1) Z24 2) Ze 3)G = {1, –1, i,-i} 4) S 5)Z

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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 24E

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QI/AI Prove that the mathematical system (s), where (o) is an usual composition map is a group? B/ Write the element of the group S, and prove that it is not abelian group?