Title: Theory / Unimportant / Math / Al gebra / Group / Generators and Relations for Discrete Groups+8/

Name: \(G\) satisfies \(g_i\)
Definition: \(g_i(S_1,\dots,S_m)=E\) holds
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Variables: \(G\) a group
\(\{S_1,\dots,S_m\}\) a set of generator
\(g_i(S_1,\dots,S_m)=E\) a relation

Name: \(G\) fulfill \(g_i\)
Definition: \(g_i(S_1,\dots,S_m)=E\) holds and furthermore, the word \(g_i(S_1,\dots,S_m)\) can not be decomposed as the concatenation of two words over \(\{S_1,\dots, S_m\}\) which are equal to \(E\)
Page: 1
Variables: \(G\) a group
\(\{S_1,\dots,S_m\}\) a set of generator
\(g_i(S_1,\dots,S_m)=E\) a relation
Index: fulfill
Example: \(\{1\}\) a generator
\(g(1)=1^q\) is fullfilled by \(\mathbb Z/q\mathbb Z\) and not by \(\mathbb Z/p\mathbb Z\) for any \(p\ne q\)