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Reduced Whitehead Group


The quotient space

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

of the Whitehead group K_1A is known as the reduced Whitehead group. Here, the element [-1] in K_1A denotes the order-2 element corresponding to the unit (-1) in GL(1,A) where GL(1,A) is the collection of 1×1 invertible matrices with coefficients in an associative ring A with unit, i.e., the collection of all units in an associative unit ring A.


See also

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

This entry contributed by Christopher Stover

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References

Milnor, J. "Whitehead Torsion." Bull. Amer. Math. Soc. 72, 358-423, 1966.

Cite this as:

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

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