9 research outputs found
Public-key cryptography and invariant theory
Public-key cryptosystems are suggested based on invariants of groups. We give
also an overview of the known cryptosystems which involve groups.Comment: 10 pages, LaTe
Groups Acting on Tensor Products
Groups preserving a distributive product are encountered often in mathematics. Examples include automorphism groups of associative and non associative rings, classical groups, and automorphisms of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be gained from an examination of the universal distributive products: tensor products. We give a detailed description of the groups preserving such tensor products over semisimple and semi primary rings, and present effective algorithms to construct generators for these groups. We also discuss applications of our methods to algorithmic problems for which all currently known methods require an exponential amount of work
Finding central decompositions of p-groups
Polynomial-time algorithms are given to find a central decomposition of
maximum size for a finite p-group of class 2 and for a nilpotent Lie ring of
class 2. The algorithms use Las Vegas probabilistic routines to compute the
structure of finite *-rings and also the Las Vegas C-MeatAxe. When p is small,
the probabilistic methods can be replaced by deterministic polynomial-time
algorithms.
The methods introduce new group isomorphism invariants including new
characteristic subgroups.Comment: 28 page
Linear groups and computation
Funding: A. S. Detinko is supported by a Marie Skłodowska-Curie Individual Fellowship grant (Horizon 2020, EU Framework Programme for Research and Innovation).We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in this class of groups are surveyed. We illustrate the solution of hard mathematical problems by computer experimentation. Possible avenues for further progress are discussed.PostprintPeer reviewe
Linear groups and computation
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for this class of groups are surveyed. We illustrate the solution of hard mathematical problems by computer experimentation. Possible avenues for further progress are discussed