Conjugacy languages in virtual graph products

نویسندگان

چکیده

In this paper we study the behaviour of conjugacy languages in virtual graph products, extending results by Ciobanu et. al. [13]. We focus primarily on products form a semi-direct product. First, twisted representatives right-angled Artin and Coxeter groups. prove regularity geodesic language for certain cases, highlight properties spherical language, depending automorphism ordering generating set. Finally, give criterion when is not unambiguous context-free products. can extend further case RAAGs, to show context-free.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Conjugacy Problem for Finite Graph Products

A finite graph product is the fundamental group of a finite graph of groups. Finite graph products with finite cyclic edge groups are shown to inherit a solvable conjugacy problem from their vertex groups under certain conditions, of which the most important is that all the edge group generators in each vertex group are powers of a common central element.

متن کامل

Conjugacy Languages in Groups

We study the regularity of several languages derived from conjugacy classes in a finitely generated group G for a variety of examples including word hyperbolic, virtually abelian, Artin, and Garside groups. We also determine the rationality of the growth series of the shortlex conjugacy language in virtually cyclic groups, proving one direction of a conjecture of Rivin. 2010 Mathematics Subject...

متن کامل

The Conjugacy Problem for Graph Products with Cyclic Edge Groups

A graph product is the fundamental group of a graph of groups Amongst the simplest examples are HNN groups and free products with amalgamation. The conjugacy problem is solvable for recursively presented graph products with cyclic edge groups over finite graphs if the vertex groups have solvable conjugacy problem and the sets of cyclic generators in them are semicritical. For graph products ove...

متن کامل

On Conjugacy of Languages

We say that two languages X and Y are conjugates if they satisfy the conjugacy equation XZ = ZY for some language Z. We study several problems associated to this equation. For example, we characterize all sets which are conjugated via a two-element biprefix set Z, as well as all two-element sets which are conjugates. Mathematics Subject Classification. 68R15, 68Q70.

متن کامل

Conjugacy growth series and languages in groups

In this paper we introduce the geodesic conjugacy language and geodesic conjugacy growth series for a finitely generated group. We study the effects of various group constructions on rationality of both the geodesic conjugacy growth series and spherical conjugacy growth series, as well as on regularity of the geodesic conjugacy language and spherical conjugacy language. In particular, we show t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Algebra

سال: 2023

ISSN: ['1090-266X', '0021-8693']

DOI: https://doi.org/10.1016/j.jalgebra.2023.06.029