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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 21E: With H and K as in Exercise 18, prove that K is a normal subgroup of HK. Exercise18: If H is a...

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Theorem 3: Finite Subgroup Test
Let H be a nonempty finite subset of a group G.
If H is closed under the operation of G, then H is a subgroup of G.

2. Provide a two-column proof of Theorem 3: Finite Subgroup Test.
3. Provide a two-column proof:
If H and K are subgroups of G, show that H > K is a subgroup of G.
3. Find a noncyclic subgroup of order 4 in U(40).

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