Goldschmidt amalgam

Symbol-free definition
A group $$G$$ is termed a Goldschmidt amalgam of subgroups $$H_1$$ and $$H_2$$ if the following hold:


 * $$ = G$$
 * $$H_1 \cap H_2$$ is normal in both $$H_1$$ and $$H_2$$
 * $$H_1$$ and $$H_2$$ share a $$p$$-Sylow subgroup for some $$p$$
 * $$F^*(M_i) = O_p(M_i)$$ for $$i = 1, 2$$