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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

Section4.5: Normal Subgroups

Problem 16E: 16. Let be a subgroup of and assume that every left coset of in is equal to a right coset of in ....

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Let H be a subgroup of a group G and S the set of all
left cosets of H in G. Show that there is a homomorphism
8:G A (S)
and the kernel of 0 is the largest normal subgroup of G which is contained
in H.

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