The Power Problem for Groups with One Defining Relator
نویسندگان
چکیده
منابع مشابه
On One-relator Inverse Monoids and One-relator Groups
It is known that the word problem for one-relator groups and for one-relator monoids of the form Mon〈A ‖ w = 1〉 is decidable. However, the question of decidability of the word problem for general one-relation monoids of the form M = Mon〈A ‖ u = v〉 where u and v are arbitrary (positive) words in A remains open. The present paper is concerned with one-relator inverse monoids with a presentation o...
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It is a well-known fact that every group G has a presentation of the form G = F/R, where F is a free group and R the kernel of the natural epimorphism from F onto G. Driven by the desire to obtain a similar presentation of the group of automorphisms Aut(G), we can consider the subgroup Stab(R) ⊆ Aut(F ) of those automorphisms of F that stabilize R, and try to figure out if the natural homomorph...
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We prove that the natural map G → Ĝ, where G is a torsionfree group and Ĝ is obtained by adding a new generator t and a new relator w , is surjective only if w is conjugate to gt where g ∈ G . This solves a special case of the surjectivity problem for group extensions, raised by Cohen [2]. AMS Classification 20E22, 20F05; 57M20, 57Q10
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Theorem 1 The word problem for any 1-relator monoids can be reduced to the left side divisibility problem for monoids M presented in 2 generators by 1 defining relation of the form aU = bV . For the solution of this problem it sufficies to find an algorithm to recognize for any word aW (or for any word bW ) whether or not it is left side divisible in M by the letter b (accordingly by the letter...
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We apply the method of Arzhantseva-Ol’shanskii to prove that for an exponentially generic (in the sense of Ol’shanskii) class of one-relator groups the isomorphism problem is solvable in at most exponential time. This is obtained as a corollary of the more general result that for any fixed integers m > 1, n > 0 there is an exponentially generic class of m-generator n-relator groups where every ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.2307/2037985