If H and K are normal subgroups of G, show that their intersection is also a normal subgroup. To do this, let b be an element of the intersection, so b is in H and b is in K. Then what can we say about gbg^{-1} because b is in the normal subgroup K? What can we say about b, because b is in the normal subgroup H? Why then is gbg^{-1} in the intersection of H and K

If H and K are normal subgroups of G, show that their intersection is also a normal subgroup. To do this, let b be an element of the intersection, so b is in H and b is in K. Then what can we say about gbg^{-1} because b is in the normal subgroup K? What can we say about b, because b is in the normal subgroup H? Why then is gbg^{-1} in the intersection of H and K

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 17E

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