The deficiency of a finite presentation <S|R> is just |S| - |R| and the deficiency of a finitely presented group G, denoted def G, is the maximum of the deficiency over all presentations of G. The deficiency of a finite group is non-positive. The Schur multiplicator of a group G can be generated by −def G generators, and G is efficient if this number is required.
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Famous quotes containing the word deficiency:
“All rejection and negation indicates a deficiency in fertility: fundamentally, if only we were good plowland we would allow nothing to go unused, and in every thing, event, and person we would welcome manure, rain, or sunshine.”
—Friedrich Nietzsche (1844–1900)
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—E.P.P., U.S. women’s magazine contributor. The Una, p. 28 ( February 1855)
“It is easier to discover a deficiency in individuals, in states, and in Providence, than to see their real import and value.”
—Georg Wilhelm Friedrich Hegel (1770–1831)