• KingGeorge
Group Theory Challenge Problem! Let $$S_n$$ be the group of permutations on $$\{1,2,...,n\}$$, and let two players play a game. Taking turns, the two players select elements one at a time from $$S_n$$. Players may only select elements that have not already been selected. The game ends when the set of selected elements generate $$S_n$$. The player who made the last move loses. Who wins the game? [HINT: Think of this problem in terms of the largest possible set of elements you can have so that you don't generate the whole group.] [HINT 2: What are the orders of the maximal subgroups?]
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