3. Let G be a group, H and K subgroups of G. (a) Prove that H NK is a subgroup of G. Give an example showing that HUK is not necessarily a subgroup. (b) Suppose that |H| = 26 and |K|= 51. Prove that HNK = {1}.

3. Let G be a group, H and K subgroups of G. (a) Prove that H NK is a subgroup of G. Give an example showing that HUK is not necessarily a subgroup. (b) Suppose that |H| = 26 and |K|= 51. Prove that HNK = {1}.

Name: Abstract algebra problem 3. Let G be a group, H and K subgroups of G.(
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Description: Abstract algebra problem 3. Let G be a group, H and K subgroups of G.(a) Prove that H N K is a subgroup of G. Give an example showing that HUKis not necessarily a subgroup.(b) Suppose that |H| = 26 and |K| == 51. Prove that HN K = {1}.

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 12E: Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order...

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3. Let G be a group, H and K subgroups of G.
(a) Prove that H N K is a subgroup of G. Give an example showing that HUK
is not necessarily a subgroup.
(b) Suppose that |H| = 26 and |K| =
= 51. Prove that HN K = {1}.

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