Iroquois in ancient times, settling in the backcountry of the Southeast United States, including what is now Tennessee. In 2010, more than 45,000 enrolled Six Nations people lived in Canada, and about 80,000 in the United States. The most common name for the confederacy, Iroquois, is of somewhat obscure origin. The first time it appears in writing is in the account of Samuel de Champlain of his journey to Tadoussac in 1603, where it occurs as "Irocois". Other spellings appearing in the earliest sources include "Erocoise", "Hiroquois", "Hyroquoise", "Irecoies", "Iriquois", "Iroquaes", "Irroquois", and "Yroquois", as the French transliterated the term into
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"