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A family of groups with nice word problems

Published online by Cambridge University Press:  09 April 2009

Verena Huber Dyson
Verena Huber Dyson
Affiliation:
University of Illinois, Chicago Circle, Chicago, Illinois, 60680, U.S.A.
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This paper is an outgrowth of my old battle with the open sentence problem for the theory of finite groups. The unsolvability of the word problem for groups (cf. [1] and [4]) entails the undecidability of the open sentence problem for the elementary theory of groups and thus strengthens the original undecidability result for this theory (cf. [7]). The fact that the elementary theory of finite groups is also undecidable (cf. [2] and [6]) therefore justifies my interest in the open sentence problem for that theory. This paper contains a construction of groups that might lead to a negative solution.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 4 , June 1974 , pp. 414 - 425
Copyright
Copyright © Australian Mathematical Society 1974

References

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[5]Huber-Dyson, V., ‘The word problem and residually finite groups’, Amer. Math. Soc. Notices 11 (1964), 743.Google Scholar
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