Radical of an algebraic group
Encyclopedia
The radical of an algebraic group is the identity component
of its maximal normal
solvable
subgroup
.
Identity component
In mathematics, the identity component of a topological group G is the connected component G0 of G that contains the identity element of the group...
of its maximal normal
Normal subgroup
In abstract algebra, a normal subgroup is a subgroup which is invariant under conjugation by members of the group. Normal subgroups can be used to construct quotient groups from a given group....
solvable
Solvable group
In mathematics, more specifically in the field of group theory, a solvable group is a group that can be constructed from abelian groups using extensions...
subgroup
Subgroup
In group theory, given a group G under a binary operation *, a subset H of G is called a subgroup of G if H also forms a group under the operation *. More precisely, H is a subgroup of G if the restriction of * to H x H is a group operation on H...
.
External links
- "Radical of a group", Encyclopaedia of Mathematics