free subgroup
11Characteristic subgroup — In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is invariant under all automorphisms of the parent group.[1][2] Because conjugation is an automorphism, every… …
12Commutator subgroup — In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.[1][2] The commutator subgroup is important because it is the smallest… …
13Pure subgroup — In mathematics, especially in the area of algebra studying the theory of abelian groups, a pure subgroup is a generalization of direct summand. It has found many uses in abelian group theory and related areas.DefinitionA subgroup S of a… …
14SQ universal group — In mathematics, in the realm of group theory, a countable group is said to be SQ universal if every countable group can be embedded in one of its quotient groups. SQ universality can be thought of as a measure of largeness or complexity of a… …
15Ping-pong lemma — In mathematics, the ping pong lemma, or table tennis lemma, is any of several mathematical statements which ensure that several elements in a group acting on a set freely generate a free subgroup of that group.HistoryThe ping pong argument goes… …
16Boundedly generated group — In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups. The property of bounded generation is also closely related with the congruence subgroup problem (see harvnb|Lubotzky|Segal|2003) …
17Bass–Serre theory — is a part of the mathematical subject of group theory that deals with analyzing the algebraic structure of groups acting by automorphisms on simplicial trees. The theory relates group actions on trees with decomposing groups as iterated… …
18Fundamental group — In mathematics, the fundamental group is one of the basic concepts of algebraic topology. Associated with every point of a topological space there is a fundamental group that conveys information about the 1 dimensional structure of the portion of …
19Banach–Tarski paradox — The Banach–Tarski paradox is a theorem in set theoretic geometry which states that a solid ball in 3 dimensional space can be split into several non overlapping pieces, which can then be put back together in a different way to yield two identical …
20Amenable group — In mathematics, an amenable group is a locally compact topological group G carrying a kind of averaging operation on bounded functions that is invariant under left (or right) translation by group elements. The original definition, in terms of a… …
