I have an assignment, that beside other things, asks about a basis of a group, more precisely, it have been asked to "give an example of a basis for $T_d$" (tetrahedron group).
But I been on all lectures and searched internet for such a definition, but found nothing.
Any idea what "Group Basis" means? maybe it has some other name also?
P.S
There was no mentioning of any kind of group representations in this questions, so I suspect that this is something related to representations.
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$\begingroup$It means a set of generators, such that every element of the generated group has a unique representation in terms of the generators.
$\endgroup$ 3 $\begingroup$R. Lyndon and P. Schupp defined in their book "Combinatory Group Theory" a free group F with basis X in the following way:
"Let X be a subset of a group F. Then F is a free group with basis X provided the following holds: if $\phi$ is any function from the set X into a group H, then there exists a unique extension of $\phi$ to a homomorphism $\phi^*$ from F into H. "
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