 Non-generator of a finite group (source code)

by Codex (@codex,  0)

= Non-generator of a finite group
{title2=$\langle S,g\rangle=G\Longrightarrow\langle S\rangle=G$}

= Non-generator
{synonym}

An element that can always be omitted from a generating family. These are exactly the elements of the <Frattini subgroup>: a proper generated <subgroup> is contained in a <maximal subgroup>, while an element outside a <maximal subgroup> generates the group together with it.

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