On one-relator inverse monoids and one-relator groups

S.I. Adjan, Defining relations and algorithmic problems for groups and semigroups, Trudy Math. Inst. Steklov 85 (1966). Adjan, 1987, Problems of equality and divisibility in semigroups with a single defining relation, Mathem. Zametki, 41, 412 Benois, 1969, Parties rationnelles du groups libre, C.R. Acad. Sci. Paris, Sér. A, 269, 1188 A.H. Clifford, G.B. Preston, The Algebraic Theory of Semigroups, Vol. 1, 1961, Vol. 2, 1967, American Mathematical Society, Providence, RI. V. Guba, On the relationship between the word problem and the divisibility problem in one relator semigroups, Russian Math. Izv. 61, 1997, in preparation. Ivanov, 1994, The free Burnside groups of sufficiently large exponents, Internat. J. Algebra Comput., 4, 1, 10.1142/S0218196794000026 Ivanov, 1998, On the hyperbolicity of small cancellation groups and one-relator groups, Trans. Amer. Math. Soc., 350, 1851, 10.1090/S0002-9947-98-01818-2 S.V. Ivanov, J.C. Meakin, On asphericity and the Freiheitssatz for certain finitely presented groups, J. Pure Appl. Algebra 159 (2001) 121–129, this issue. Lallement, 1977, On monoids presented by a single relation, J. Algebra, 32, 370, 10.1016/0021-8693(74)90146-X Lallement, 1979 Lyndon, 1977 Magnus, 5274, Das Identitätsproblem für Gruppen mit einer definierenden Relation, Math. Ann., 105, 1931 W. Magnus, J. Karras, D. Solitar, Combinatorial Group Theory, Wiley Interscience, New York, 1966. Margolis, 1993, Inverse monoids, trees and context-free languages, Trans. Amer. Math. Soc., 335, 259 Margolis, 1986, Some decision problems for inverse monoid presentations, 99 Munn, 1974, Free inverse semigroups, Proc. London Math. Soc., 29, 385, 10.1112/plms/s3-29.3.385 Newman, 1968, Some results on one-relator groups, Bull. Amer. Math. Soc., 74, 568, 10.1090/S0002-9904-1968-12012-9 A.Yu. Ol'shanskii, Geometry of Defining Relations in Groups, Nauka, Moscow, 1989 (English translation in: Math and Its Applications (Soviet series), Vol. 70, Kluwer, Dordrecht, 1991). Petrich, 1984 Schupp, 1976, A strengthened Freiheitssatz, Math. Ann., 221, 73, 10.1007/BF01434965 Silva, 1992, Rational languages and inverse monoid presentations, Internat. J. Algebra Comput., 2, 187, 10.1142/S0218196792000128 Stephen, 1990, Presentations of inverse monoids, J. Pure Appl. Algebra, 63, 81, 10.1016/0022-4049(90)90057-O Stephen, 1993, Inverse monoids and rational subsets of related groups, Semigroup Forum, 46, 98, 10.1007/BF02573550 Watier, 1997, On the word problem for single relation monoids with an unbordered relator, Internat. J. Algebra Comput., 7, 749, 10.1142/S0218196797000332 Zhang, 1992, A short proof of a theorem of Adjan, Proc. AMS, 116, 1, 10.1090/S0002-9939-1992-1092933-6