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jango_IN_DTOWN
 one year ago
Subgroup + permutation problem
jango_IN_DTOWN
 one year ago
Subgroup + permutation problem

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1familiar with the cycle notation ? dw:1444581237571:dw

jango_IN_DTOWN
 one year ago
Best ResponseYou've already chosen the best response.1yes dw:1444581322888:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Ah, so is it given that \((1,2)\in S_3\) ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444581438396:dw

jango_IN_DTOWN
 one year ago
Best ResponseYou've already chosen the best response.1no i assumed it to be S3 since the next two contains 3, we are not given about the symmetry group

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1since \(\alpha\) exists in the subgroup, \(\alpha^2, \alpha^3, \ldots \) must also exist in the group. \(\alpha^2 = ?\)

jango_IN_DTOWN
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444581538927:dw

jango_IN_DTOWN
 one year ago
Best ResponseYou've already chosen the best response.1the identity permutation

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1so we have \(\alpha^2 = e\), therefore the subgroup generated by \((1,2)\) is : \(\{e,\alpha\}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1you may express the same in cycle notation as \(\{(1), (1,2)\}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1try working ii similarly, just consider all the powers of given permutation

jango_IN_DTOWN
 one year ago
Best ResponseYou've already chosen the best response.1we will stop when the identity permutation is reached

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1elements will be repeated if you continue, notice that \(\alpha^n =e \implies \alpha^{n+1}=\alpha \)

jango_IN_DTOWN
 one year ago
Best ResponseYou've already chosen the best response.1Yes I got it.. Thanks..
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