Please help construct the operational table Given that ge al

Please help construct the operational table.

Given that g={e, alpha ,beta, gamma} is a group with identity e and alpha^2 = beta^2= gamma^2 = e, construct the operation table for G. (All elements in G are distinct).

Solution

1. By identity every elements on diagonal are iqual to e

2. First row operate by (x,e) = x

3. First column operate by (x,e) = x

finally

4. All elements in G are distinct, so (x,y) = z, for example; (gamma,beta) = alpha

	e	alpha	beta	gamma
e	e	alpha	beta	gamma
alpha	alpha	e	gamma	beta
beta	beta	gamma	e	alpha
gamma	gamma	beta	alpha	e