TY - GEN
T1 - Groups with a recursively enumerable irreducible word problem
AU - Rino Nesin, Gabriela
AU - Thomas, Richard M.
N1 - The final authenticated version is available online at https://doi.org/10.1007/978-3-642-40164-0_27
PY - 2013/1/1
Y1 - 2013/1/1
N2 - The notion of the word problem is of fundamental importance in group theory. The irreducible word problem is a closely related concept and has been studied in a number of situations; however there appears to be little known in the case where a finitely generated group has a recursively enumerable irreducible word problem. In this paper we show that having a recursively enumerable irreducible word problem with respect to every finite generating set is equivalent to having a recursive word problem. We prove some further results about groups having a recursively enumerable irreducible word problem, amongst other things showing that there are cases where having such an irreducible word problem does depend on the choice of finite generating set.
AB - The notion of the word problem is of fundamental importance in group theory. The irreducible word problem is a closely related concept and has been studied in a number of situations; however there appears to be little known in the case where a finitely generated group has a recursively enumerable irreducible word problem. In this paper we show that having a recursively enumerable irreducible word problem with respect to every finite generating set is equivalent to having a recursive word problem. We prove some further results about groups having a recursively enumerable irreducible word problem, amongst other things showing that there are cases where having such an irreducible word problem does depend on the choice of finite generating set.
U2 - 10.1007/978-3-642-40164-0_27
DO - 10.1007/978-3-642-40164-0_27
M3 - Conference contribution with ISSN or ISBN
VL - 8070
T3 - Lecture Notes in Computer Science
SP - 283
EP - 292
BT - International Symposium on Fundamentals of Computation Theory
PB - Springer
CY - Berlin, Heidelberg
T2 - International Symposium on Fundamentals of Computation Theory
Y2 - 1 January 2013
ER -