4 Quotient groups

In the previous section, when attempting to pretend that a 3

×

3

×

3 Rubik’s

cube is a 2

×

2

×

2 one, we came up with the cosets

form a group. We also said that this is not the case for arbitrary subgroup

but only for subgroups that satisfy

Ha

. Before we prove these, we first

study these subgroups a bit.