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Direct sums are defined for a number of different sorts of mathematical objects, including subspaces, matrices, modules, and groups. The matrix direct sum is defined by ...

A generalized quadrangle is a generalized polygon of order 4. An order-(s,t) generalized quadrangle contains s+1 points in each line and has t+1 lines through every point, ...

Vassiliev invariants, discovered around 1989, provided a radically new way of looking at knots. The notion of finite type (a.k.a. Vassiliev) knot invariants was independently ...

The direct sum of modules A and B is the module A direct sum B={a direct sum b|a in A,b in B}, (1) where all algebraic operations are defined componentwise. In particular, ...

An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the ...

A group in which any decreasing chain of distinct subgroups terminates after a finite number.

A normalizer of a nontrivial Sylow p-subgroup of a group G.

A group that has a primitive group action.

A group G is quasi-unipotent if every element of G of order p is unipotent for all primes p such that G has p-group rank >=3.

L is a subnormal subgroup of H if there is a "normal series" (in the sense of Jordan-Hölder) from L to H.