In mathematical finite group theory, a block, sometimes called Aschbacher block, is a subgroup giving an obstruction to Thompson factorization and pushing up. Blocks were introduced by Michael Aschbacher.
Definition
A group L is called short if it has the following properties (Aschbacher & Smith 2004, definition C.1.7):
Foote, Richard (1980), "Aschbacher blocks", The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), Proc. Sympos. Pure Math., vol. 37, Providence, R.I.: Amer. Math. Soc., pp. 37–42, MR0604554
Solomon, Ronald (1980), "Some results on standard blocks", The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), Proc. Sympos. Pure Math., vol. 37, Providence, R.I.: Amer. Math. Soc., MR0604555