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A free group of rank k clearly has subgroups of every rank less than k. Less obviously, a (nonabelian!) free group of rank at least 2 has subgroups of all countable ranks. The commutator subgroup of a free group of rank k > 1 has infinite rank; for example for F(a,b), it is freely generated by the commutators [a m, b n] for non-zero m and n.
Free energy suppression (or new energy suppression) is a conspiracy theory that technologically viable, pollution-free, no-cost energy sources are being suppressed by ...
For Real chronology; It's a Natural Thang (1994) Free (1996) ... "The Saddest Song I Ever Heard" Released: February 22, 1997; Free is the second album by R&B group ...
More generally, one can construct the free algebra R E on any set E of generators. Since rings may be regarded as Z-algebras, a free ring on E can be defined as the free algebra Z E . Over a field, the free algebra on n indeterminates can be constructed as the tensor algebra on an n-dimensional vector space.
Big Generator is the twelfth studio album by English progressive rock band Yes, released on 28 September 1987 by Atco Records, their last album of new music for the label. [4] After touring in support of their previous album, 90125 (1983), which saw the band move from progressive rock towards a pop-oriented and commercially accessible direction ...
The free-piston linear generator (FPLG) uses chemical energy from fuel to drive magnets through a stator and converts this linear motion into electric energy. Because of its versatility, low weight and high efficiency, it can be used in a wide range of applications, although it is of special interest to the mobility industry as range extenders for electric vehicles.
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