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 -