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.
Read more about this topic: Presentation Of A Group
Famous quotes containing the word deficiency:
“If a man is a good lawyer, a good physician, a good engineer ... he may be a fool in every other capacity. But no deficiency or mistake of judgment is forgiven to a woman ... and should she fail anywhere, if she has any scientific attainment, or artistic faculty, instead of standing her interest as an excuse, it is censured as an aggravation and offence.”
—E.P.P., U.S. women’s magazine contributor. The Una, p. 28 ( February 1855)
“Free verse leaves out the meter and makes up
For the deficiency by church intoning.
Free verse, so called, is really cherished prose....”
—Robert Frost (1874–1963)
“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)