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<Text-field style="Heading 1" layout="Normal">gerar,</Text-field>
<Text-field style="Text" layout="Normal"><Font italic="true">v.</Font> <Font bold="true">1.</Font><Font encoding="UTF-8"> para fornecer um crit\303\251rio preciso para a participa\303\247\303\243o em um conjunto, na forma de um algor\303\255tmo cuja aplica\303\247\303\243o recursivamente produz todos e somente os membros do conjunto. Por exemplo, as regras de forma\303\247\303\243o geram todos e somente suas express\303\265es bem formadas; os elementos da base em um espa\303\247o vetorial gera o espa\303\247o. </Font><Font bold="true">2.</Font><Font encoding="UTF-8"> (de um subconjunto de uma estrutura assim como um anel, grupo ou m\303\263dulo) para permitir que todos os elementos do grupo sejam constru\303\255dos pela aplica\303\247\303\243o recursiva das opera\303\247\303\265es definidas na estrutura dos membros dos subconjuntos; ent\303\243o, a estrutura \303\251 contida no fechamento do conjunto de seus </Font><Font italic="true">geradores</Font><Font encoding="UTF-8"> sob essas opera\303\247\303\265es. Por exemplo, o conjunto de todas as transposi\303\247\303\265es gera o grupo sim\303\251trico e o conjunto  de todo ciclo-3 gera o grupo alternado. Uma estrutura </Font><Font italic="true">finitamente gerada</Font><Font encoding="UTF-8">  \303\251 o fechamento de um conjunto finito de </Font><Font italic="true">geradores</Font>. Claramente, qualquer <Hyperlink linktarget="Dictionary:Definition/basis" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">base</Font></Hyperlink><Font encoding="UTF-8"> de um espa\303\247o vetorial gera  o espa\303\247o.</Font></Text-field>
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