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Abstract
The notion of central series for groups with action on itself is introduced. An analogue of Witt's construction is given for such groups. A certain condition is found for the action and the corresponding category is defined. It is proved that the above construction defines a functor from this category to the category of Lie–Leibniz algebras and in particular to Leibniz algebras; also the restriction of this functor on the category of groups leads us to Lie algebras and gives the result of Witt.
Key words and phrases:: Central series; groups; groups with action on itself; Lie algebras; Leibniz algebras; Lie–Leibniz algebras
Received: 2002-06-04
Published Online: 2010-02-25
Published in Print: 2002-December
© Heldermann Verlag
