On Weighted Geodesics in Groups
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AbstractA word W in a group G is a geodesic (weighted geodesic) if W has minimum length (minimum weight with respect to a generator weight function α) among all words equal to W. For finitely generated groups, the word problem is equivalent to the geodesic problem. We prove: (i) There exists a group G with solvable word problem, but unsolvable geodesic problem, (ii) There exists a group G with a solvable weighted geodesic problem with respect to one weight function α1, but unsolvable with respect to a second weight function α2. (iii) The (ordinary) geodesic problem and the free-product geodesic problem are independent.
2002 ◽
Vol 12
(01n02)
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pp. 213-221
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1982 ◽
Vol 14
(1)
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pp. 43-44
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2017 ◽
Vol 27
(07)
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pp. 819-830
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2015 ◽
Vol 26
(01)
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pp. 79-98
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Keyword(s):
2013 ◽
Vol 23
(05)
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pp. 1099-1114
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