Beauville structures in finite p-groups

Fernandez-Alcober, Gustavo A.
Gul, Sukran
We study the existence of (unmixed) Beauville structures in finite p-groups, where p is a prime. First of all, we extend Catanese's characterisation of abelian Beauville groups to finite p-groups satisfying certain conditions which are much weaker than commutativity. This result applies to all known families of p-groups with a good behaviour with respect to powers: regular p-groups, powerful p-groups and more generally potent p-groups, and (generalised) p-central p-groups. In particular, our characterisation holds for all p-groups of order at most pP, which allows us to determine the exact number of Beauville groups of order p(5), for p >= 5, and of order p(6), for p >= 7. On the other hand, we determine which quotients of the Nottingham group over F-p are Beauville groups, for an odd prime p. As a consequence, we give the first explicit infinite family of Beauville 3-groups, and we show that there are Beauville 3-groups of order 3(n) for every n >= 5.


Beauville structures in p-groups
Gül, Şükran; Ercan, Gülin; Fernández-Alcober, Gustavo Adolfo; Department of Mathematics (2016)
Given a finite group G and two elements x, y in G, we denote by Sigma(x,y) the union of all conjugates of the cyclic subgroups generated by x, y and xy. Then G is called a Beauville group of unmixed type if the following conditions hold: (i) G is a 2-generator group. (ii) G has two generating sets {x1,y1} and {x2, y2} such that Sigma (x1, y1) intersection Sigma(x2, y2) is 1. In this case, {x1, y1} and {x2, y2} are said to form a Beauville structure for G. The main purpose of this thesis is to extend the kn...
A socio-spatial approach to the question of class and consciousness formation in a local setting: the case of Bursa industrial workers
Erengezgin, B Çavlan; Şengül, Hüseyin Tarık; Department of Urban Policy Planning and Local Governments (2007)
The aim of this thesis is to explore the class and consciousness formation in a local setting by also developing and applying a theoretical framework which allow us to study the interaction of locus of class consciousness with the other loci of consciousness formation such as the community and the state. Such an approach is also grounded in the belief that a relational understanding of these processes requires us to take spatial dynamics such as local dependency, spatial fix and fixity and mobility into acc...
Classification of Automorphism Groups of Rational Elliptic Surfaces
Karayayla, Tolga (null; 2011-01-06)
In this paper, we give a classification of (regular) automorphism groups of relatively minimal rational elliptic surfaces with section over the field which have non-constant J-maps. The automorphism group of such a surface B is the semi-direct product of its Mordell–Weil group and the subgroup of the automorphisms preserving the zero section σ of the rational elliptic surface B. The configuration of singular fibers on the surface determines the Mordell–Weil group as has been shown by Oguiso and Shioda (...
Normalizers in homogeneous symmetric groups
Güven, Ülviye Büşra; Kuzucuoğlu, Mahmut; Department of Mathematics (2017)
We study some properties of locally finite simple groups, which are the direct limit of finite (finitary) symmetric groups of (strictly) diagonal type. The direct limit of the finite (finitary) symmetric groups of strictly diagonal type is called textbf{homogeneous (finitary) symmetric groups}. In cite{gkk}, Kegel, Kuzucuou{g}lu and myself studied the structure of centralizer of finite groups in the homogeneous finitary symmetric groups. Instead of strictly diagonal embeddings, if we have diagonal embedding...
On the existence of kappa-existentially closed groups
Kegel, Otto H.; Kaya, Burak; Kuzucuoğlu, Mahmut (2018-09-01)
We prove that a κ-existentially closed group of cardinality λ exists whenever κ ≤ λ are uncountable cardinals with λ^{<κ} = λ. In particular, we show that there exists a κ-existentially closed group of cardinalityκ for regular κ with 2^{<κ} = κ. Moreover, we prove that there exists noκ-existentially closed group of cardinality κ for singular κ. Assuming thegeneralized continuum hypothesis, we completely determine the cardinalsκ ≤ λ for which a κ-existentially closed group of cardinality λ exists
Citation Formats
G. A. Fernandez-Alcober and S. Gul, “Beauville structures in finite p-groups,” JOURNAL OF ALGEBRA, pp. 1–23, 2017, Accessed: 00, 2020. [Online]. Available: