Decision problems for groups and semigroups

Адян, Сергей Иванович; Durnev, V. G.

doi:10.1070/rm2000v055n02abeh000267

Cited by 43 publications

(49 citation statements)

References 56 publications

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“…The following theorem was first proved by Adian in [1] for finite presentations. Later, it was generalized by Remmers to any Adian presentation, in [6], by using a geometric approach.…”

Section: The Word Problem For Adian Semigroups Adian Inverse Semigromentioning

confidence: 99%

“…In the LG X|R , we obtain an edge by joining the vertex labeled by the prefix letter of u with the vertex labeled by the prefix letter of v for all (u, v) ∈ R. The RG X|R is constructed dually by joining the vertex labeled by the suffix letter of u with the vertex labeled by suffix letter of v for all (u, v) ∈ R. If there is no cycle in the left and the right graph of a presentation then the presentation is called a cycle free presentation or an Adian presentation. These presentation were first studied by S. I. Adian [1], where is shown that the finitely presented Adian semigroups Sg X|R embeds in the corresponding Adian Gp X|R . Latter in [6] John H. Remmers generalized this result to any Adian presentation and proved that an Adian semigroup Sg X|R embeds in the corresponding Adian group Gp X|R .…”

Section: Introductionmentioning

confidence: 99%

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The word problem for some classes of Adian inverse semigroups

Inam

2017

Semigroup Forum

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“…The following theorem was first proved by Adian in [1] for finite presentations. Later, it was generalized by Remmers to any Adian presentation, in [6], by using a geometric approach.…”

Section: The Word Problem For Adian Semigroups Adian Inverse Semigromentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The word problem for some classes of Adian inverse semigroups

Inam

2017

Semigroup Forum

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“…This is not necessarily true for non-commutative monoids, so for this class of monoids the question if there is a group G such that M can be embedded in G arises. Adian, in [1], gives a partial answer to this question: he gives a sufficient condition for embeddability of the monoid in the group with the same presentation. In what follows, we will describe Adian's criteria for embeddability.…”

Section: 1mentioning

confidence: 99%

“…In [1], Adian gave a sufficient condition on the presentation of a monoid for its embeddability in a group, which is very simple to check.…”

Section: Introductionmentioning

confidence: 99%

Rewriting Systems and Embedding of Monoids in Groups

Chouraqui¹

2009

Groups – Complexity – Cryptology

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Abstract. In this paper, a connection between rewriting systems and embedding of monoids in groups is found. We consider monoids and groups with the same presentation and we show that if the group admits a complete rewriting system ℜ, which satisfies the condition that each rule in ℜ with positive left-hand side has a positive right-hand side, then the monoid embeds in the group if and only if ℜ satisfies an additional condition. As an example, we give a simple proof that right angled Artin monoids embed in the corresponding right angled Artin groups. This is a special case of the well-known result of Paris [11] that Artin monoids embed in their groups.

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“…In investigating the (S1),(S2),(S3) conditions of Theorem 3 we found that the corresponding groups R(r, n, k, h) are free products of copies of F (3, 12, 4) (for (S1)), of F (3, 8, 2) (for (S2)), and of either F (3, 6, 1) or R(3, 6, 5, 2) (for (S3)). Simplifying the presentations in GAP [12] reveals that F (3, 12, 4) = x 2 , x 5 | (x 2 x 5 ) 37 ∼ = Z 37 * Z and that (writing a = x 1 …”

Section: Proofmentioning

confidence: 99%