High Quality Content by WIKIPEDIA articles! In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a recursively presented group G is the algorithmic problem of deciding whether two words represent the same element. Although it is common to speak of the word problem for the group G strictly speaking it is a presentation of the group that does or does not have solvable word problem. Given two finite presentations P and Q of a group G, P has solvable word problem if and only if Q does. So in this case no confusion is caused by speaking of the word problem for G. When the group is recursively presented but not finitely presented, the distinction becomes important.