Central extensions of rank 2 groups and applications

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چکیده

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Central extensions of rank 2 groups and applications

We show that the universal central extensions of the little projective group of any Moufang polygon is precisely the Steinberg group obtained from its defining commutator relations, provided the defining structure is not too small. As an application, we get that also the universal central extensions of the little projective group of any 2-spherical Moufang twin building is precisely the Steinbe...

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DEFINITION. A group G is called a universal locally finite central extension of A provided that the following conditions are satisfied. (i) A <= (G (the centre of G). (ii) G is locally finite. (iii) (/1-injectivity). Suppose that A <= B <= D with A a (D, that D/A is finite, and that q>: B -> G is an ^-isomorphism (that is, q>{a) = a for all as A). Then there exists an extension q>: D -*• G of (...

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ژورنال

عنوان ژورنال: Forum Mathematicum

سال: 2009

ISSN: 0933-7741,1435-5337

DOI: 10.1515/forum.2009.001