One thing to note about groups is that it is not always the case that a â cents b = b â cents a for every a and b in the group .
In other words , the result of combining element a with element b need not yield the same result as combining element b with element a ; the equation a â cents b = b â cents a may not always be true . This equation does always hold in the group of integers under addition , because a + b = b + a for any two integers ( commutativity of addition ) .