Question

Modern Algebra optional standard: I can compute Cayley tables of quotient groups Let G=D₈, and let H=⟨r²⟩. Write down the Cayley table for G/H.

Answer 1

To compute the Cayley table for the quotient group G/H, multiply the elements of G with the elements of the cosets of H. The Cayley table represents the quotient group G/H.

Step-by-step explanation:

To compute the Cayley table for the quotient group G/H, we need to start with the elements of G and the cosets of H. In this case, G is the dihedral group D₈, and H is the subgroup generated by the element r². To create the Cayley table, we multiply the elements of G with the elements of the cosets of H, obtaining the quotient group G/H.

Here is an example of how the Cayley table for G/H could be computed:

rHr²HsHsrHrsHsr²Hrs²Hsr³HrHrHr²HsHsrHrsHsr²Hrs²Hsr³Hr²Hr²HHsr²Hrs²Hsr³HsrHrsHsHsHsHsr²HHsrHrsHsr³Hrs²HsrHsrHsrHrs²HsrHrsHsr³HrsHsr²HsHrsHrsHsr³HrsHsr²HsHsrHrsHsr²Hsr²Hsr²HsrHsr³HrsHsr²Hrs²Hsr³HHrs²Hrs²HrsHsr²HsrHrs²Hsr³HHsrHsr³Hsr³HsHsrHrs²Hsr³HHsrHrsH