- #1
Mr Davis 97
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Here is a problem statement: Let ##H## be a proper subgroup of a finite group ##G##. Prove that the union of the conjugates of ##H## is not all of ##G##.
I have proven this statement by considering the action of ##G## on ##\mathcal{P}(G)##. But this leads me to wonder: In the problem statement is there any reason why ##H## must be a subgroup? Am I right in saying that the statement seems true for any ##S## such that ##S\subset G##?
I have proven this statement by considering the action of ##G## on ##\mathcal{P}(G)##. But this leads me to wonder: In the problem statement is there any reason why ##H## must be a subgroup? Am I right in saying that the statement seems true for any ##S## such that ##S\subset G##?