From: neumann@vax.ox.ac.uk To: GROUP-PUB-FORUM@maths.bath.ac.uk Date: Sat, 18 Feb 1995 10:40:42 +0000 Dear All, Can anyone remind me---or, more likely, tell me---about the group with presentation $\langle a, b : ba = a^2b^2 \rangle$? It has obvious infinite cyclic and tetrahedral quotient groups. Are there many references to it in the literature? Tony Crilly has pointed out to me that Cayley took a side-swipe at it in 1878. Rather typically, what Cayley wrote was pretty inconsequential. He simply observed that in a non-abelian group generated by two elements satisfying that relation not every element can be expressed in the form $a^pb^q$. Best wishes, $\Pi$eter Neumann Queen's: 18.ii.95