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This development of group theory was started at the Newton Institute in August 1995. It was prompted by the need to have conventional mathematical proofs to test the work of Yann Coscoy on producing text from the Coq proof objects. It turns out that it is also a good testing ground for naive set theory. I followed the notations and numbering of W.R. Scott, Group Theory, Dover Books ISBN 0-486-65377-3 Theorem 1.6.4 takes only three lines to prove in that book... Gilles Kahn January 1996