Example

The product Z/2Z × Z/2Z of two copies of the additive group Z/2Z consists of e = (0,0), a = (1,0), b = (0,1) and c = (1,1). Note that each nonidentity element has order 2 (that is, x² = e) and that ab = c, ac = b, bc = a. Don't get confused by the multiplicative notation for the binary operation!