# The word problem in polycyclic groups is elementary

F. B. Cannonito; R. W. Gatterdam

Compositio Mathematica (1973)

- Volume: 27, Issue: 1, page 39-45
- ISSN: 0010-437X

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topCannonito, F. B., and Gatterdam, R. W.. "The word problem in polycyclic groups is elementary." Compositio Mathematica 27.1 (1973): 39-45. <http://eudml.org/doc/89177>.

@article{Cannonito1973,

author = {Cannonito, F. B., Gatterdam, R. W.},

journal = {Compositio Mathematica},

language = {eng},

number = {1},

pages = {39-45},

publisher = {Noordhoff International Publishing},

title = {The word problem in polycyclic groups is elementary},

url = {http://eudml.org/doc/89177},

volume = {27},

year = {1973},

}

TY - JOUR

AU - Cannonito, F. B.

AU - Gatterdam, R. W.

TI - The word problem in polycyclic groups is elementary

JO - Compositio Mathematica

PY - 1973

PB - Noordhoff International Publishing

VL - 27

IS - 1

SP - 39

EP - 45

LA - eng

UR - http://eudml.org/doc/89177

ER -

## References

top- [1] L. Auslander: On a problem of Phillip Hall. Annals of Math., 86 (1967), 112-116. Zbl0149.26904MR218454
- [2] W.W. Boone: Word problems and recursively enumerable degrees of unsolvability. Annals of Math., 83 (1966), 520-591. Zbl0173.01204MR201499
- [3] W.W. Boone: Word problems and recursively enumerable degrees of unsolvability. A sequel on finitely presented groups. Annals of Math., 84 (1966), 49-84. Zbl0173.01301MR201500
- [4] F.B. Cannonito: Hierarchies of computable groups and the word problem. J. Symbolic Logic, 31 (1966), 376-392. Zbl0178.32502MR224471
- [5] F.B. Cannonito and R.W. Gatterdam: The computability of group constructions, Part I. Word Problems, Boone, Cannonito, Lyndon eds., North-Holland Publishing Company, Amsterdam (1973). Zbl0274.02017MR346063
- [6] F.B. Cannonito and R.W. Gatterdam: The word problem and power problem in 1-relator groups is primitive recursive (submitted for publication). Zbl0335.02029
- [7] C.R.J. Clapham: Finitely presented groups with word problem of arbitrary degree of insolubility. Proc. London Math. Soc., 14 (1964), 633-676. Zbl0232.20063MR179238
- [8] R.W. Gatterdam: Embeddings of primitive recursive computable groups (submitted for publication).
- [9] R.W. Gatterdam: The computability of group constructions, Part II Bull. Australian Math. Soc., 8 (1973) 27-60. Zbl0243.02036MR446939
- [10] S.C. Kleene: Introduction to Metamathematics. Van Nostrand, Princeton, New Jersey (1952). Zbl0047.00703MR51790
- [11] S. Maclane: Homology. Springer-Verlag, Berlin (1963). Zbl0133.26502MR349792

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