a finite group $g$ satisfies the on-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes $m$ and $n$ are either equal or have a common divisor a prime power. taeri conjectured that an insoluble group satisfying this condition is isomorphic to $s times a$ where $a$ is abelian and $s cong psl_2(q)$ for $q in {4,8}$. we confirm this conjecture.

Suppose that a group G acts transitively on the points of P, a finite non-Desarguesian projective plane. We prove first that the Sylow 2subgroups of G are cyclic or generalized quaternion; we then prove that if G is insoluble then G/O(G) is isomorphic to SL2(5) or SL2(5).2. MSC(2000): 20B25, 51A35.

1. When myosin is exposed to a typical denaturing agent (acid) it becomes insoluble and its SH groups are activated. 2. The same number of active SH groups is found in the soluble myosin of resting muscle as in the insoluble myosin of muscle in rigor. No activation of SH groups accompanies the formation of insoluble protein in rigor. 3. When the insoluble myosin of muscle in rigor is treated wi...