This is question 53[tex]\gamma[/tex]. Given a group G of transformations that acts on X... and a subgroup of G, Go (g * x = x for all x for each g in Go), show that the quotient group G/Go acts effectively on X.(adsbygoogle = window.adsbygoogle || []).push({});

A group G "acts effectively" on X, if g * x = x for all x implies that g = e, where g is a member of G.

I don't see how the quotient group G/Go can act on X... Each member of the quotient group, is itself a set of transformations. For example, take Go which is a member of G/Go. It seems to me that Go * x (where x belongs to X) is undefined, since Go is not a one to one correspondence from X to X (each member of Go is, but Go itself isn't).

I'd appreciate any help. Thanks.

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# Another question from Elements of Abstract Algebra by Clark - transformation groups

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