**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Schreier's lemma

Summary

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.
Statement
Suppose H is a subgroup of G, which is finitely generated with generating set S, that is, G = \langle S\rangle.
Let R be a right transversal of H in G. In other words, R is (the image of) a section of the quotient map G \to H\backslash G, where H\backslash G denotes the set of right cosets of H in G.
We make the definition that given g∈G, \overline{g} is the chosen representative in the transversal R of the coset Hg, that is,
:g\in H\overline{g}.
Then H is generated by the set
:{rs(\overline{rs})^{-1}|r\in R, s\in S}.
Hence, in particular, Schreier'

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related people

Related publications

Related units

No results

No results

No results

Related courses

Related lectures

Related concepts

No results

No results

No results