The following groups have property FA: • A finitely generated torsion group; • SL3(
Z); • The Schwarz group \left\langle{ a,b : a^A = b^B = (ab)^C = 1 }\right\rangle for integers
A,
B,
C ≥ 2; • SL2(
R) where
R is the ring of integers of an
algebraic number field which is not
Q or an
imaginary quadratic field. The following groups do not have property FA: • SL2(
Z); • SL2(
RD) where
RD is the ring of integers of an imaginary quadratic field of discriminant not −3 or −4. ==References==