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Dec 23, 2015 · Let $G$ be a finite group. Sylow's Third Theorem claims that the number of Sylow $p$-subgroups of $G$ is …

@simplicity: Like almost every book I have seen on algebraic topology, Hatcher's text is a graduate text. Your other questions posted …

Invariance of domain at least in statement seems a simple result. I mean, the first time I saw the statement I thought: "the proof can't …

In an infinite dimensional Banach space, does a compact subset have to be finite dimensional? I know it cannot contain any infinite …

May 16, 2015 · That's (my) definition of ex e x ${e}^{x}$. You have another one? If so, please specify. Although this may not be …

$ab{b}^{-1}{a}^{-1}=e$ but it not true of every group that abba = abb−1a−1 = (ab)(ab)−1 = abab a b b a = a b b 1 a 1 = (a b) (a b) 1 = a …

There are so many real-world examples of this it's hard to pick one. Basically any time you are doing one computation and then …

In most cases, if you’re asking the question of why something is true, well, that’s the whole point of mathematics, and you should try …

Aug 31, 2017 · @wanderingmathematician I think in category theory, direct product corresponds to product, and direct sum …

Jun 23, 2022 · Question: prove Γ(a)Γ(b) = Γ(a + b)B(a, b) Γ (a) Γ (b) = Γ (a + b) B (a, b) $\mathrm{\Gamma }(a)\mathrm{\Gamma …