1,720,961 research outputs found
Overgroups of subsystem subgroups in exceptional groups: inside a sandwich
Full text linkThe current paper is an addition to the previous paper by author, where the
overgroup lattice of the elementary subsystem subgroup of the
Chevalley group for a large enough root subsystem was
studied. Now we study the connection between the elementary subgroup
given by the net of ideals of the ring and the stabilizer
of the corresponding Lie subalgebra of the Chevalley algebra. In
particular, we prove that under a certain condition the subgroup
is normal in , and we also study some properties
of the corresponding quotient group.Comment: 23 pages, no figures, to appear in St. Petersburg math. Journa
Bounded reduction for Chevalley groups of types and
Full text linkWe prove that an element from the Chevalley group of type or over
a polynomial ring with coefficients in a small-dimensional ring can be reduced
to an element of certain proper subsystem subgroup by a bounded number of
elementary root elements. The bound is given explicitly. This result is an
effective version of the early stabilisation of the corresponding
-functor. We also give part of the proof of similar hypothesis for .Comment: 32 pages, 7 figures, submitted to "European Journal of Mathematics".
arXiv admin note: substantial text overlap with arXiv:2106.1269
Verbal width in arithmetic Chevalley groups
Full text linkWe prove that the width of any word in a simply connected Chevalley group of rank at least 2 over the ring that is a localisation of the ring of integers in a number field is bounded by a constant that depends only on the root system and on the degree of the number field.11 page
Overgroups of subsystem subgroups in exceptional groups: 2A1-proof
Full text linkIn the present paper we prove a weak form of sandwich classification for the
overgroups of the subsystem subgroup of the Chevalley group
where is a simply laced root sysetem and is its
sufficiently large subsystem. Namely we show that for any such an overgroup
there exists a unique net of ideals of the ring such that
where
is an elementary subgroup associated with the net and
is a corresponding subalgebra of the Chevalley Lie algebra.Comment: 25 pages, to appear in St.Petersburg Math Journa
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Commutator lengths in general linear group over a skew-field
Full text linkWe give an upper and lower estimate for the maximal commutator length of a
noncentral element of the elementary subgroup of the general linear group over
a skew-field based on the maximal commutator length of an element of the
multiplicative group of that skew-field.Comment: 12 pages, to be published in Journal of Mathematical Science
Width of SL(n,O_S,I)
Full text linkWe give an estimate for the width of the congruence subgroup
in Tits--Vaserstein generators, where is a
localisation of the ring of integers in a number field . We assume that
either has a real embedding, or the ideal is prime to the number of
roots of unity in .Comment: 16 pages, no figures, submitted to Communications in Algebr
Overgroups of subsystem subgroups in exceptional groups: nonideal levels
Full text linkIn the present paper, we practicaly complete the solution of the problem on
the description of overgroups of the subsystem subgroup in the
Chevalley group over the ring , where is a simply laced
root system, and is its large enough subsystem. Namely we define
objects called levels, and show that for any such an overgroup there exists
a unique level such that , where is an
elementary subgroup defined by the level , and is
the corresponding Lie subalgebra in the Chevalley algebra. Unlike all the
previous papers, now levels can be more complicated objects that the nets of
ideals.Comment: 33 pages, no figures, to appear in St.Petersburg Math Journa
On countable isotypic structures
Full text linkWe obtain several results concerning the concept of isotypic structures.
Namely we prove that any field of finite transcendence degree over a prime
subfield is defined by types; then we construct isotypic but not isomorphic
structures with countable underlying sets: totally ordered sets, fields, and
groups. This answers an old question by B. Plotkin for groups.Comment: 6 pages, Published in journal of Groups, Complexity, Cryptolog
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