Black Box White Arrow
release_mmvjy6jd5vabzerjqrb2qeqxjy
by
Alexandre Borovik, Şükrü Yalçinkaya
2014
Abstract
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 categories of black boxes and their morphisms. This
makes new classes of black box problems accessible. For example, we can enrich
black box groups by actions of outer automorphisms.
As an example of application of this technique, we construct Frobenius maps
on black box groups of untwisted Lie type in odd characteristic (Section 6) and
inverse-transpose automorphisms on black box groups encrypting
(P)SL_n(F_q).
One of the advantages of our approach is that it allows us to work in black
box groups over finite fields of big characteristic. Another advantage is
explanatory power of our methods; as an example, we explain Kantor's and
Kassabov's construction of an involution in black box groups encrypting
SL_2(2^n).
Due to the nature of our work we also have to discuss a few methodological
issues of the black box group theory.
The paper is further development of our text "Fifty shades of black"
[arXiv:1308.2487], and repeats parts of it, but under a weaker axioms for black
box groups.
In text/plain
format
Archived Files and Locations
application/pdf 1.4 MB
file_swmff6jzavgsnjupcbwantxoqe
|
arxiv.org (repository) web.archive.org (webarchive) |
1404.7700v1
access all versions, variants, and formats of this works (eg, pre-prints)