49 citations · 185 across the 47 of their papers we have counts for
27 papers · 1 filter
The Şiş Kebap Theorem: A Generic Identification Theorem for Groups of Finite Morley Rank
Ayşe Berkman, Alexandre V. Borovik
This paper contains a new version of a final identification theorem for the `generic' groups of finite Morley rank, developing further the results of [4] and [5]. It is prepared fo…
Groups of finite Morley rank with a generically multiply transitive action on an abelian group
Ayşe Berkman, Alexandre Borovik
We investigate the configuration where a group of finite Morley rank acts definably and generically -transitively on an elementary abelian -group of Morley rank , where $p…
Finite group actions on abelian groups of finite Morley rank
Alexandre Borovik
This paper develops some general results about actions of finite groups on (infinite) abelian groups in the finite Morley rank category. They are linked to a range of problems on g…
Natural representations of black box groups encrypting
Alexandre Borovik, Şükrü Yalçınkaya
Given a global exponent for a black box group encrypting , where is an unknown finite field of unknown odd characteristic, we…
Locally finite groups of finite centraliser dimension
Alexandre Borovik, Ulla Karhumäki
We describe structure of locally finite groups of finite centraliser dimension.
Groups of finite Morley rank with a generically sharply multiply transitive action
Ayşe Berkman, Alexandre Borovik
We prove that if is a group of finite Morley rank which acts definably and generically sharply -transitively on a connected abelian group of Morley rank with no invo…
Homomorphic encryption and some black box attacks
Alexandre Borovik, Şükrü Yalçınkaya
This paper is a compressed summary of some principal definitions and concepts in the approach to the black box algebra being developed by the authors. We suggest that black box alg…
Rank 3 Bingo
Alexandre Borovik, Adrien Deloro
We classify irreducible actions of connected groups of finite Morley rank on abelian groups of Morley rank 3.
Adjoint representations of black box groups
Alexandre Borovik, Şükrü Yalçınkaya
Given a black box group encrypting over an unknown field of unknown odd characteristic and a global exponent for $\mathsf…
Black Box White Arrow
Alexandre Borovik, Şükrü Yalçinkaya
The present paper proposes a new and systematic approach to the so-called black box group methods in computational group theory. Instead of a single black box, we consider categori…
Construction of some subgroups in black box groups and
Alexandre Borovik, Şükrü Yalçınkaya
For the black box groups encrypting , odd, we propose an algorithm constructing a subgroup encrypting and subfield subgroups of . We also…
Fifty shades of black
Alexandre Borovik, Şükrü Yalçınkaya
The paper proposes a new and systematic approach to the so-called black box group methods in computational group theory. As the starting point of our programme, we construct Froben…
Steinberg presentations of black box classical groups in small characteristics
Alexandre Borovik, Sukru Yalcinkaya
The main component of (constructive) recognition algorithms for black box groups of Lie type in computational group theory is the construction of unipotent elements. In the existin…
Groups of Finite Morley Rank with a Pseudoreflection Action
Ayse Berkman, Alexandre Borovik
In this work, we give two characterisations of the general linear group as a group of finite Morley rank acting on an abelian connected group of finite Morley rank definabl…
Uniqueness Cases in Odd Type Groups of Finite Morley Rank, Revisited
Alexandre Borovik, Jeffrey Burdges, Ali Nesin
The paper contains versions of the Strong Embedding Theorem and the Uniqueness Subgroup Theorem for groups of finite Morley rank and odd type which are needed for the study of perm…
A Generic Identification Theorem for Groups of Finite Morley Rank, Revisited
Ayse Berkman, Alexandre Borovik
This paper contains a stronger version of a final identification theorem for the `generic' groups of finite Morley rank.
The Finitary Andrews-Curtis Conjecture
Alexandre V. Borovik, Alexander Lubotzky, Alexei G. Myasnikov
The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis gr…
Construction of Curtis-Phan-Tits system in black box classical groups
Alexandre Borovik, Sukru Yalcinkaya
We present a polynomial time Monte-Carlo algorithm for finite simple black box classical groups of odd characteristic which constructs all root -subgroups associate…
Generic complexity of the Conjugacy Problem in HNN-extensions and algorithmic stratification of Miller's groups
Alexandre V. Borovik, Alexei G. Myasnikov, Vladimir N. Remeslennikov
We discuss time complexity of The Conjugacy Problem in HNN-extensions of groups, in particular, in Miller's groups. We show that for "almost all", in some explicit sense, elements,…
The Conjugacy Problem in Amalgamated Products I: Regular Elements and Black Holes
Alexandre V. Borovik, Alexei G. Myasnikov, Vladimir N. Remeslennikov
We discuss the time complexity of the word and conjugacy search problems for free products of groups and with amalgamation over a subgroup . We stratif…
A New Trichotomy Theorem
Alexandre Borovik, Jeffrey Burdges
We show that a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank has normal 2-rank at most two, which is a tameness free…
Uniqueness cases in odd type groups of finite Morley rank
Alexandre Borovik, Jeffrey Burdges, Ali Nesin
Here we analyze a proper 2-generated core in a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank. We ultimately show tha…
Multiplicative measures on free groups
Alexandre V. Borovik, Alexei G. Myasnikov, Vladimir N. Remeslennikov
We introduce a family of atomic measures on free groups generated by no-return random walks. These measures are shown to be very convenient for comparing "relative sizes" of subgro…
Measuring sets in infinite groups
Alexandre V. Borovik, Alexei G. Myasnikov, Vladimir Shpilrain
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a…