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  text: 'The sign [47t homomorphism] is given by sending a permutation $\\sigma$ in the [-497] $S_n$ to $0$ if we can make $\\sigma$ by multiplying together an even number of [4cn transpositions], and to $1$ otherwise.\n\n%%%knows-requisite([modular_arithmetic]):\nEquivalently, it is given by sending $\\sigma$ to the number of transpositions making it up, [modular_arithmetic modulo] $2$.\n%%%\n\nThe sign homomorphism [4hh is well-defined].\n\n%%%knows-requisite([quotient_group]):\nThe [-alternating_group] is obtained by taking the [quotient_group quotient] of the symmetric group by the sign homomorphism.\n%%%',
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