Cliques and Groups

Extract

Mr. Parrack's paper on cliques [in the Gazette of February 1966, pp. 43-46] links up with some results which I obtained in 1962 on “ double-identities ”. [Mimeographed copies of the paper are available for any who wish them.]

Briefly, the simplest kind of double-identity is an equation which, like:

is an identity in any additively-written abelian group when “ o ” is replaced by “ + ” and, also, when “ o ” is replaced by “ - ”. More precisely, an (e, o)-double identity is an equation between terms constructed from variables, “ o ”, and a constant, “ e ”, which is an identity when “ e ” is replaced by “ 0 ” and “ o ” is replaced by “ + ” or by “ - ”.