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Elements Of Modern Algebra

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 15E

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answer part d, e and f

In the group G = Z24, let H =(4) and K = (8).
(a) State the Third Isomorphism Theorem.
(b) List the cosets in G/H, showing the elements in each coset.
(c) List the cosets in G/K, showing the elements in each coset.
(d) List the cosets in H/K, showing the elements in each coset.

(e) List the cosets in (G/K)/(H/K), showing the elements in each coset.
(f) Give the correspondence between G/H and (G/K)/(H/K) described in the proof of the
theorem in (a).

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