Easy S and L groups

This is the published version, also available here: http://dx.doi.org/10.1090/S0002-9939-1980-0553388-2. First published in Amer. Math. Soc. in 1979, published by the American Mathematical Society.We give a simple proof that the existence of strong S or L spaces implies the existence of strong S or L groups; in fact the algebraic structure can be varied quite a bit. We also construct, under CH, S and L groups whose squares are neither S nor L