- #1
snipez90
- 1,101
- 5
Homework Statement
http://math.uchicago.edu/~dc/teaching/254/254_problem_set_05.pdf"
Homework Equations
H a subgroup of G implies HH = H, where HH is the direct product.
The Attempt at a Solution
For the forward direction, don't we just have |A| = 0 or 1? I think |A| = 0 should be excluded since then A is the empty set, which makes proving the forward direction kind of nonsensical.
For the reverse direction, if A = aH = Hb, then AA = aHHb = aHb, and can't we just send each ah in aH (= A) to ahb in aHb (= AA) for the bijection?
This seems too easy, so I've likely made an oversight. Thanks in advance.
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