True or False:

If H and K are subgroups of G, then is a subgroup of G.

If is a subgroup of G for all , then is a subgroup of G.

Explanations would be greatly appreciated.

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- Mar 17th 2010, 01:00 PMjameselmore91Union of Subgroups
True or False:

If H and K are subgroups of G, then is a subgroup of G.

If is a subgroup of G for all , then is a subgroup of G.

Explanations would be greatly appreciated. - Mar 17th 2010, 02:10 PMDinkydoe
You only need to verify that these sets are groups,

that is

(1)

(2)

((3) associativity is automatically satisfied)

These are trivial exercises. Keep the definition of intersections in mind.

The same goes for

(Edit: What you wrote was not the right symbol for Union. The union symbol is . However the excercise is the same) - Mar 17th 2010, 02:57 PMDrexel28
- Mar 17th 2010, 03:34 PMDinkydoe
Yes, true. However on second thought, the poster mustve meant -intersection of sub-groups-

- Mar 17th 2010, 03:43 PMjameselmore91
My mistake, I did mean to say intersection of Subgroups