# Definition of Subgroup. Meaning of Subgroup. Synonyms of Subgroup

Here you will find one or more explanations in English for the word Subgroup. Also in the bottom left of the page several parts of wikipedia pages related to the word Subgroup and, of course, Subgroup synonyms and on the right images related to the word Subgroup.

## Definition of Subgroup

Subgroup
Subgroup Sub"group`, n. (Biol.) A subdivision of a group, as of animals. --Darwin.

## Meaning of Subgroup from wikipedia

- as "H is a subgroup of G". The trivial subgroup of any group is the subgroup {e} consisting of just the identity element. A proper subgroup of a 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...
- 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...
- 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...
- 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...
- Subgroup analysis refers to repeating the analysis of a study within subgroups of subjects defined by a subgrouping variable (e.g. smoking status defining...
- mathematics and physics. Lie groups were first found by studying matrix subgroups G {\displaystyle G} contained in GL n ( R ) {\displaystyle {\text{GL}}_{n}(\mathbb...
- algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup. For example, in the general...
- {\displaystyle p} , a Sylow p-subgroup (sometimes p-Sylow subgroup) of a group G {\displaystyle G} is a maximal p {\displaystyle p} -subgroup of G {\displaystyle...