# nLab Malcev group

## Definition

A Malcev group is a filtered group $G=F_1 G\supset F_2 G\supset\cdots$ such that

Morphisms of Malcev groups are morphisms of filtered groups?.

## Properties

The category of Malcev groups is equivalent to the category of rational complete Hopf algebras. See there for more information.

## References

• А. И. Мальцев, Нильпотентные группы без кручения, Изв. АН СССР. Сер. матем. 13:3 (1949), 201–212. PDF.

• Daniel Quillen, Rational homotopy theory, Annals of Mathematics 90:2 (1969), 205. doi.

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