Definition:Generator of Group/Also denoted as
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Generator of Group: Also denoted as
If $S$ is a singleton, that is: $S = \set x$, then we can (and usually do) write $G = \gen x$ for the group generated by $\set x$ rather than $G = \gen {\set x}$.
Some sources use the notation $\operatorname {gp} \set S$ for the subgroup generated by $S$.
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 5.3$. Subgroup generated by a subset