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In topology, a branch of mathematics, for \( i\geq 2 \), the i-th homotopy group with coefficients in an abelian group G of a based space X is the pointed set of homotopy classes of based maps from the Moore space of type (G,i) to X, and is denoted by \( \pi _{i}(X;G) \) .[1] For \( i\geq 3 \) , \( \pi _{i}(X;G) \) is a group. Note that \( {\displaystyle \pi _{i}(X;\mathbb {Z} )} \) are the usual homotopy groups of X.
References

Weibel 2013, Ch. IV. Definition 2.1

Weibel, Charles (2013). "The K-book: An introduction to algebraic K-theory".

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