scholarly journals Automorphism groups and Picard groups of additive full subcategories

2010 ◽  
Vol 107 (1) ◽  
pp. 5 ◽  
Author(s):  
Naoya Hiramatsu ◽  
Yuji Yoshino
Keyword(s):  
Automorphism Group ◽  
Direct Product ◽  
Full Subcategory ◽  
Automorphism Groups ◽  
Commutative Rings ◽  
Picard Group ◽  
Picard Groups

We study category equivalences between additive full subcategories of module categories over commutative rings. And we are able to define the Picard group of additive full subcategories. The aim of this paper is to study the properties of the Picard groups and show that the automorphism group of an additive full subcategory is a semi-direct product of the Picard group with the group of algebra automorphisms of the ring.

scholarly journals Semidirect product groups with Abelian automorphism groups

1987 ◽  
Vol 42 (1) ◽  
pp. 84-91 ◽  
Author(s):  
M. J. Curran
Keyword(s):  
Automorphism Group ◽  
Direct Product ◽  
Cyclic Group ◽  
Semidirect Product ◽  
Dihedral Group ◽  
Automorphism Groups ◽  
Infinite Family ◽  
Central Automorphism ◽  
Nonabelian Group ◽  
Semidirect Product Groups

AbstractMiller's group of order 64 is a smallest example of a nonabelian group with an abelian automorphism group, and is the first in an infinite family of such groups formed by taking the semidirect product of a cyclic group of order 2m (m ≥ 3) with a dihedral group of order 8. This paper gives a method for constructing further examples of non abelian 2-groups which have abelian automorphism groups. Such a 2-group is the semidirect product of a cyclic group and a special 2-group (satisfying certain conditions). The automorphism group of this semidirect product is shown to be isomorphic to the central automorphism group of the corresponding direct product. The conditions satisfied by the special 2-group are determined by establishing when this direct product has an abelian central automorphism group.

Algebras with Transitive Automorphism Groups

1986 ◽  
Vol 29 (2) ◽  
pp. 224-226
Author(s):  
L. G. Sweet ◽  
J. A. MacDougall
Keyword(s):  
Automorphism Group ◽  
Direct Product ◽  
Automorphism Groups ◽  
Finite Dimensional Algebra ◽  
Dimensional Algebra ◽  
Transitive Automorphism ◽  
Cyclic Groups ◽  
Finite Dimensional

AbstractLet A be a finite dimensional algebra (not necessarily associative) over a field, whose automorphism group acts transitively. It is shown that K = GF(2) and A is a Kostrikin algebra. The automorphism group is determined to be a semi-direct product of two cyclic groups. The number of such algebras is also calculated.

scholarly journals Automorphism group of the variant of the lattice of partitions of a finite set

2020 ◽  
pp. 115-119
Author(s):  
O. G. Ganyushkin ◽  
O. O. Desiateryk
Keyword(s):  
Automorphism Group ◽  
Wreath Product ◽  
Direct Product ◽  
Automorphism Groups ◽  
Symmetric Groups ◽  
Natural Generalization ◽  
Generating Sets ◽  
Generalized Wreath Product ◽  
Finite Set

In this paper we consider variants of the lattice of partitions of a finite set and study automorphism groups of this variants. We obtain irreducible generating sets for of the lattice of partitions of a finite set. We prove that the automorphism group of the variant of the lattice of partitions of a finite set is a natural generalization of the wreath product. The first multiplier of this generalized wreath product is the direct product of the wreaths products, such that depends on the type of the variant generating partition and the second is defined by the certain set of symmetric groups.

scholarly journals Serre’s Property (FA) for automorphism groups of free products

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Naomi Andrew
Keyword(s):  
Automorphism Group ◽  
Free Product ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Free Products ◽  
Cyclic Groups ◽  
Link Type ◽  
Open Case

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

Automorphism groups of arithmetically saturated models

2006 ◽  
Vol 71 (1) ◽  
pp. 203-216 ◽  
Author(s):  
Ermek S. Nurkhaidarov
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Open Subgroup ◽  
Peano Arithmetic ◽  
Standard System ◽  
Permutation Groups ◽  
Saturated Model ◽  
Saturated Models ◽  
Homogeneous Set ◽  
Image Position

In this paper we study the automorphism groups of countable arithmetically saturated models of Peano Arithmetic. The automorphism groups of such structures form a rich class of permutation groups. When studying the automorphism group of a model, one is interested to what extent a model is recoverable from its automorphism group. Kossak-Schmerl [12] show that if M is a countable, arithmetically saturated model of Peano Arithmetic, then Aut(M) codes SSy(M). Using that result they prove:Let M1. M2 be countable arithmetically saturated models of Peano Arithmetic such that Aut(M1) ≅ Aut(M2). Then SSy(M1) = SSy(M2).We show that if M is a countable arithmetically saturated of Peano Arithmetic, then Aut(M) can recognize if some maximal open subgroup is a stabilizer of a nonstandard element, which is smaller than any nonstandard definable element. That fact is used to show the main theorem:Let M1, M2be countable arithmetically saturated models of Peano Arithmetic such that Aut(M1) ≅ Aut(M2). Then for every n < ωHere RT2n is Infinite Ramsey's Theorem stating that every 2-coloring of [ω]n has an infinite homogeneous set. Theorem 0.2 shows that for models of a false arithmetic the converse of Kossak-Schmerl Theorem 0.1 is not true. Using the results of Reverse Mathematics we obtain the following corollary:There exist four countable arithmetically saturated models of Peano Arithmetic such that they have the same standard system but their automorphism groups are pairwise non-isomorphic.

scholarly journals On a Theorem of Bers, with Applications to the Study of Automorphism Groups of Domains

2016 ◽  
Vol 59 (2) ◽  
pp. 346-353
Author(s):  
Steven Krantz
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Holomorphic Functions ◽  
Biholomorphic Equivalence ◽  
Algebras Of Holomorphic Functions

AbstractWe study and generalize a classical theoremof L. Bers that classifies domains up to biholomorphic equivalence in terms of the algebras of holomorphic functions on those domains. Then we develop applications of these results to the study of domains with noncompact automorphism group

AUTOMORPHISMS OF CERTAIN NILPOTENT LIE ALGEBRAS OVER COMMUTATIVE RINGS

2007 ◽  
Vol 17 (03) ◽  
pp. 527-555 ◽  
Author(s):  
YOU'AN CAO ◽  
DEZHI JIANG ◽  
JUNYING WANG
Keyword(s):  
Automorphism Group ◽  
Commutative Ring ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Commutative Rings ◽  
Nilpotent Lie Algebras ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Positive Roots ◽  
Nilpotent Subalgebra

Let L be a finite-dimensional complex simple Lie algebra, Lℤ be the ℤ-span of a Chevalley basis of L and LR = R⊗ℤLℤ be a Chevalley algebra of type L over a commutative ring R. Let [Formula: see text] be the nilpotent subalgebra of LR spanned by the root vectors associated with positive roots. The aim of this paper is to determine the automorphism group of [Formula: see text].

scholarly journals AUTOMORPHISM GROUPS OF RANDOMIZED STRUCTURES

2017 ◽  
Vol 82 (3) ◽  
pp. 1150-1179 ◽  
Author(s):  
TOMÁS IBARLUCÍA
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Original Structure ◽  
Polish Groups ◽  
Separable Models

AbstractWe study automorphism groups of randomizations of separable structures, with focus on the ℵ0-categorical case. We give a description of the automorphism group of the Borel randomization in terms of the group of the original structure. In the ℵ0-categorical context, this provides a new source of Roelcke precompact Polish groups, and we describe the associated Roelcke compactifications. This allows us also to recover and generalize preservation results of stable and NIP formulas previously established in the literature, via a Banach-theoretic translation. Finally, we study and classify the separable models of the theory of beautiful pairs of randomizations, showing in particular that this theory is never ℵ0-categorical (except in basic cases).

scholarly journals Direct product of automorphism groups of colored graphs

2004 ◽  
Vol 283 (1-3) ◽  
pp. 81-86 ◽  
Author(s):  
Mariusz Grech ◽  
Andrzej Kisielewicz
Keyword(s):  
Direct Product ◽  
Automorphism Groups ◽  
Colored Graphs

scholarly journals A note on subgroups of automorphism groups of full shifts

2016 ◽  
Vol 38 (4) ◽  
pp. 1588-1600 ◽  
Author(s):  
VILLE SALO
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Endomorphism Monoid ◽  
Direct Products ◽  
Free Products ◽  
Group Case ◽  
Sofic Shift ◽  
Full Shift

We discuss the set of subgroups of the automorphism group of a full shift and submonoids of its endomorphism monoid. We prove closure under direct products in the monoid case and free products in the group case. We also show that the automorphism group of a full shift embeds in that of an uncountable sofic shift. Some undecidability results are obtained as corollaries.

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