In finite group theory, a branch of mathematics, 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 : L has no subgroup of index 2 The generalized Fitting subgroup F*(L) is a 2-group O2(L) The subgroup U = [O2(L), L] is an elementary abelian 2-group in the center of O2(L) L/O2(L) is quasisimple or of order 3 L acts irreducibly on U/CU(L)
An example of a short group is the semidirect product of a quasisimple group with an irreducible module over the 2-element field F2
A block of a group G is a short subnormal subgroup.
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