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can you Construct cayley table for dihedral six-gon given the element is {e,a,a^2,a^3,a^4,a^5,f,af,a^2f,a^3f,a^4f,a^5f}. then show that dihedral six-gon (D6) is non commutative based on the cayley table

can you Construct cayley table for dihedral six-gon given the element is {e,a,a^2,a^3,a^4,a^5,f,af,a^2f,a^3f,a^4f,a^5f}. then show that dihedral six-gon (D6) is non commutative based on the cayley table

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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can you Construct cayley table for dihedral six-gon given the element is {e,a,a^2,a^3,a^4,a^5,f,af,a^2f,a^3f,a^4f,a^5f}.

then show that dihedral six-gon (D6) is non commutative based on the cayley table

the image is the example of the cayley table:

Cayley table of D4 e ro ro ro rel re2 re3 re4 e e ro n² n3 rel re2 re3 re4 ro ro r² r³ e re2 re3 re4 rel 25252 r² r² r³ e ro re3 re4 rel re2 n3³ e ro 22 re4 re1 re2 re3 rel rel re4 re3 re2 e ro re2 re2 re1 re4 re3 n² e CCE re3 re3 re2 rel re4 n² r² e r.³ re4 re4 re3 re2 rel || ગ r² r² e
Transcribed Image Text:Cayley table of D4 e ro ro ro rel re2 re3 re4 e e ro n² n3 rel re2 re3 re4 ro ro r² r³ e re2 re3 re4 rel 25252 r² r² r³ e ro re3 re4 rel re2 n3³ e ro 22 re4 re1 re2 re3 rel rel re4 re3 re2 e ro re2 re2 re1 re4 re3 n² e CCE re3 re3 re2 rel re4 n² r² e r.³ re4 re4 re3 re2 rel || ગ r² r² e
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