Thus option (c) is correct.Let G be a group with G| = 96. Suppose H and K are subgroups of G with H] = 12and K| = 16. Then(a) HOK = {e}(b) HnK # {e}(c) HOK is Abelian(d) HnK is not Abelian

for abelian group -: condition -: 1 closure ,2 associative , 3 -: identity , 4 -: inverse ,5-:…

Answered: Thus option (c) is correct. Let G be 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 11E: Let be a group of order 24. If is a subgroup of , what are all the possible orders of ?

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Thus option (c) is correct. Let G be a group with G| = 96. Suppose H and K are subgroups of G with [H = 12 and K| = 16. Then (a) HOK = {e} %3D (b) HOK + {e} (c) HOK is Abelian (d) HnK is not Abelian