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 . Here, the element denotes the element of group order dividing 2 corresponding to the unit where is the set of invertible matrices with coefficients in an associative ring with unit, 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, 358-423, 1966.

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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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