Definition of Subgroup. Meaning of Subgroup. Synonyms of Subgroup

- In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group...
- In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation...
- commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group. The commutator subgroup is important...
- the term maximal subgroup is used to mean slightly different things in different areas of algebra. In group theory, a maximal subgroup H of a group G is...
- Parabolic subgroup may refer to: a parabolic subgroup of a reflection group a subgroup of an algebraic group that contains a Borel subgroup This disambiguation...
- subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example is the subgroup of...
- In the theory of abelian groups, the torsion subgroup AT of an abelian group A is the subgroup of A consisting of all elements that have finite order...
- p} , a Sylow p-subgroup (sometimes p-Sylow subgroup) of a finite group G {\displaystyle G} is a maximal p {\displaystyle p} -subgroup of G {\displaystyle...
- said to have no small subgroup if there exists a neighborhood U {\displaystyle U} of the identity that contains no nontrivial subgroup of G . {\displaystyle...
- S\subseteq G} fixed under conjugation. The centralizer and normalizer of S are subgroups of G. Many techniques in group theory are based on studying the centralizers...