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单词 ConjugateStabilizerSubgroups
释义

conjugate stabilizer subgroups


Let be a right group action of G on a set M. Then

Gαg=g-1Gαg

for any αM and gG. 11Gα is the stabilizerMathworldPlanetmath subgroupMathworldPlanetmathPlanetmath of αM.

Proof:

xGαgα(gx)=αgα(gxg-1)=αgxg-1Gαxg-1αg

and therefore Gαg=g-1Gαg.

Thus all stabilizer subgroups for elements of the orbit G(α) of αare conjugate to Gα.

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更新时间:2025/5/4 14:03:32