Related papers: The theorems on freedom for relatively free groups…
In this paper we prove the theorem on freedom for free products with a single relation (analogous with the well-known result of Magnus) and a generalized Freiheitssatz for free products (analogous with the well-known result of Romanovski)
In this paper we prove the theorem on freedom for relatively free groups with a single relation (analogous with the well-known result of Magnus) and the theorem on freedom for relatively free Lie algebras with a single relation (analogous…
In this paper we prove the theorem on freedom for relatively free Lie algebras with a single relation (analogous with the well-known result of Shirshov) and a generalized Freiheitssatz for relatively free Lie algebras (analogous with the…
In this paper we prove the theorem on freedom for free sums of Lie algebras with a single relation (analogous with the well-known result of Shirshov) and a generalized Freiheitssatz for free sums of Lie algebras (analogous with the…
The known facts about solvability of equations over groups are considered from a more general point of view. A generalized version of the theorem about solvability of unimodular equations over torsion-free groups is proved. In a special…
In this paper we establish necessary condition for the Freiheitsatz of Magnus can be extended to free pro-${\it p}$-groups
The main result includes as special cases on the one hand, the Gerstenhaber--Rothaus theorem (1962) and its generalisation due to Nitsche and Thom (2022) and, on the other hand, the Brodskii--Howie--Short theorem (1980--1984) generalising…
This is an English translation of three articles, originally written in German, by Wilhelm Magnus (1907--1990). The articles are from 1930, 1931, and 1932, respectively, and were the first articles published on one-relator group theory. The…
We prove the Freiheitssatz for right-symmetric algebras and the decidability of the word problem for right-symmetric algebras with a single defining relation. We also prove that two generated subalgebras of free right-symmetric algebras are…
In this paper we study a group G which is the quotient of a free product of groups by the normal closure of a word that is contained in a in a subgroup which has the form of a generalised triangle group. We use known properties of…
We prove the decidability of the elementary theory of a free group.
We generalise a key result of one-relator group theory, namely Magnus's Freiheitssatz, to partially commutative groups, under sufficiently strong conditions on the relator. The main theorem shows that under our conditions, on an element $r$…
In this paper, we mainly discuss some generalized metric properties and the character of the free paratopological groups, and extend several results valid for free topological groups to free paratopological groups.
We obtain some results related to Romanoff's theorem.
In this paper, we generalise Magnus' Freiheitssatz and solution to the word problem for one-relator groups by considering one relator quotients of certain classes of right-angled Artin groups and graph products of locally indicable…
We provide an elementary proof that subgroups of free groups are free via group actions.
We prove a version of Hrushovski's socle lemma for rigid groups in an arbitrary simple theory.
We prove the Freiheitssatz for Poisson algebras in characteristic zero. We also give a proof of the tameness of automorphisms for two generated free Poisson algebras and prove that an analogue of the commutator test theorem is equivalent to…
We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.
In this work the author studies the property close to property of order separability.