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Sylow's Theorem and the arithmetic of binomial coefficients


Abstract


We present a result on the existence and the number of subgroups of any given prime-power order containing an arbitrarily fixed subgroup in a finite group (see also [2]). Our proof is an extension of Krull's generalization ([1],1961)of Sylow's theorem, which leads us to consider a new concept (the conditioned binomial coefficient) of independent combinatorial interest.

DOI Code: 10.1285/i15900932v22n1p83

Keywords: Sylow's Theorem; Binomial Coefficients

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