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Shijie Gu
Shijie Gu
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Is the following statement true: Any surjective homomorphism $f:G\to H$ of groups with equal rank maps aevery minimal generating system $x$ of $G$ to a minimal generating system $y$ of $H$? "Minimal generating set" means "generating set of minimal cardinality". Is it only valid for finite rank? How about infinite rank?

Is the following statement true: Any surjective homomorphism $f:G\to H$ of groups with equal rank maps a minimal generating system $x$ of $G$ to a minimal generating system $y$ of $H$? Is it only valid for finite rank? How about infinite rank?

Is the following statement true: Any surjective homomorphism $f:G\to H$ of groups with equal rank maps every minimal generating system $x$ of $G$ to a minimal generating system $y$ of $H$? "Minimal generating set" means "generating set of minimal cardinality". Is it only valid for finite rank? How about infinite rank?

Source Link
Shijie Gu
Shijie Gu
  • 2.1k
  • 1
  • 15
  • 18

Surjective group homomorphism sending minimal generating system to minimal generating system

Is the following statement true: Any surjective homomorphism $f:G\to H$ of groups with equal rank maps a minimal generating system $x$ of $G$ to a minimal generating system $y$ of $H$? Is it only valid for finite rank? How about infinite rank?