Reduced Whitehead Group

The reduced Whitehead group is the quotient group

$K^__1A=K_1A/{0,[-1]}$

of the Whitehead group by the subgroup generated by (Milnor 1966, p. 362). Here, the element corresponds to the unit and has order dividing 2. The general linear group is the set of invertible matrices with coefficients in an associative ring with multiplicative identity, i.e., the set of all units in an associative unit ring .

See also

General Linear Group, Group Order, Quotient Group, Ring, Unit, Unit Ring, Whitehead Group

Portions of this entry contributed by Christopher Stover

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References

Milnor, J. "Whitehead Torsion." Bull. Amer. Math. Soc. 72, 358-426, 1966. https://doi.org/10.1090/S0002-9904-1966-11484-2.

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Reduced Whitehead Group

Cite this as:

Weisstein, Eric W., with contributions by Christopher Stover. "Reduced Whitehead Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ReducedWhiteheadGroup.html

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