subgroup
subset of a mathematical group that forms a group itself
weakly normal subgroup
subgroup H of a group G such that, for every g∈G, if Hᵍ ≤ N_G(H), then g ∈ N_G(H)
thin subgroup
given a real semisimple algebraic group G, a descrete Zariski-dense subgroup of G(ℝ) with infinite covolume
centralizer
subgroup of a group G that each leaves invariant each element of a given subset of a G-set
Hall subgroup
subgroup whose order is coprime to its index
perfect core
the largest perfect subgroup of a group
permutation group
group whose operation is composition of permutations
observable subgroup
algebraic subgroup of a linear algebraic group whose every finite-dimensional rational representation arises as the restriction to the subgroup of a finite-dimensional rational representation of the whole group
stabilizer subgroup
subgroup that fixes a given point with respect to a group action
maximal subgroup
Term in mathematics
multiplicative group
group of invertible elements of a ring with respect to multiplication
subnormal subgroup
subgroup such that there is a finite chain of subgroups of the group, each one normal in the next, from the original subgroup to the entire group
lattice
discrete subgroup in a locally compact topological group
torsion subgroup
subgroup of A consisting of all elements that have finite order
Borel subgroup
maximal Zariski-closed connected solvable algebraic subgroup of an algebraic group
congruence subgroup
matrix group
peripheral subgroup
a certain subgroup of the fundamental group of the complementary space
verbal subgroup
subgroup of a group that is generated by all elements that can be formed by substituting group elements for variables in a given set of words
Cartan subgroup
maximal connected Abelian subgroup
subring
subset of a ring that forms a ring itself
crystallographic point group
classification system for crystals
normalizer
subgroup of a group G that fixes a given subset of a G-set
submodule
additive subgroup of a module closed under scalar multiplication
pure subgroup
a subgroup S of a group G such that, whenever an element of S has an nth root in G, it necessarily has an nth root in S