# Category: Lemmas in group theory

Schreier's lemma
In mathematics, Schreier's lemma is a theorem in group theory used in the Schreier–Sims algorithm and also for finding a presentation of a subgroup.
Burnside's lemma
Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy–Frobenius lemma, orbit-counting theorem, or The Lemma that is not Burnside's, is a result in group theory which is often
Three subgroups lemma
In mathematics, more specifically group theory, the three subgroups lemma is a result concerning commutators. It is a consequence of Philip Hall and Ernst Witt's eponymous identity.
Mautner's lemma
In mathematics, Mautner's lemma in representation theory states that if G is a topological group and π a unitary representation of G on a Hilbert space H, then for any x in G, which has conjugates yxy
Goursat's lemma
Goursat's lemma, named after the French mathematician Édouard Goursat, is an algebraic theorem about subgroups of the direct product of two groups. It can be stated more generally in a (and consequent
Zassenhaus lemma
In mathematics, the butterfly lemma or Zassenhaus lemma, named after Hans Zassenhaus, is a technical result on the lattice of subgroups of a group or the of a module, or more generally for any modular
Ping-pong lemma
In mathematics, the ping-pong lemma, or table-tennis lemma, is any of several mathematical statements that ensure that several elements in a group acting on a set freely generates a free subgroup of t
Frattini's argument
In group theory, a branch of mathematics, Frattini's argument is an important lemma in the structure theory of finite groups. It is named after Giovanni Frattini, who used it in a paper from 1885 when