Iroquois Finger Lakes region, and upstate New York along the St. Lawrence River area downstream to today's Montreal. French, Dutch and British colonists in both New France (Canada) and the what became the Thirteen Colonies recognized a need to gain favor with the Iroquois people, who occupied a significant portion of lands west of colonial settlements. Their first relations with them were for fur trading, which was favorable and became lucrative to both sides. The colonists also sought to establish positive relations to secure their settlement borders. For nearly 200 years the Iroquois were a powerful factor in North American colonial
Word problem for groups would expect it to be difficult to prove as the mapping from presentations to simple groups would have to be non-recursive. The following has been proved by Bernhard Neumann and Angus Macintyre: What is remarkable about this is that the algebraically closed groups are so wild that none of them has a recursive presentation. The oldest result relating algebraic structure to solvability of the word problem is Kuznetsov's theorem: To prove this let ⟨"X"|"R"⟩ be a recursive presentation for "S". Choose "a" ∈ S such that "a" ≠ 1 in "S". If "w" is a word on the generators "X"