Sylow subgroup

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Sylow subgroup

[¦sī‚lō ′səb‚grüp]
(mathematics)
A subgroup H of a given group G such that the order of H is p n , where p is a prime and n is an integer, and p n is the highest power of p dividing the order of G.
References in periodicals archive ?
He covers preliminaries, Sylow theorems, solvable groups and nilpotent groups, group extensions, Hall subgroups, Frobenius groups, transfer, characters, finite subgroups of GLn, and small groups.
Other topics include polynomials, factorization in integral domains, p-groups and the Sylow theorems, Galois theory, and finiteness conditions for rings and modules.
Nicholson starts with a review of proofs, sets, mappings and equivalences, then in 11 chapters covers integers and permutations, groups, rings, polynomials, factorization in integral domains, fields, modules over principal ideal domains, p-groups and the Sylow theorems, series of subgroups, Galois theory and finiteness conditions for rings and modules.