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Extensions by a Free Abelian Group of Rank 2

J. S. Rose
Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences
Vol. 71 (1971), pp. 19-26
Published by: Royal Irish Academy
Stable URL: http://www.jstor.org/stable/20488704
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Extensions by a Free Abelian Group of Rank 2
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Abstract

It has been shown that for any group K with non-trivial centre, there is a non-split extension of K by some abelian group A. There is evidence for expecting that A may be chosen to be free abelian of rank 2. A general criterion for all extensions of a group by a free abelian group of rank 2 to split is established. Then it is shown that a group with non-trivial centre may in fact have all its extensions by a free abelian group of rank 2 split.

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