Injectivity on the Set of Conjugacy Classes of Some Monomorphisms between Artin Groups
نویسنده
چکیده
There are well-known monomorphisms between the Artin groups of finite type An, Bn = Cn and affine type Ãn−1, C̃n−1. The Artin group A(An) is isomorphic to the (n + 1)strand braid group Bn+1, and the other three Artin groups are isomorphic to some subgroups of Bn+1. The inclusions between these subgroups yield monomorphisms A(Bn) → A(An), A(Ãn−1) → A(Bn) and A(C̃n−1) → A(Bn). There are another type of monomorphisms A(Bd)→ A(Amd−1), A(Bd)→ A(Bmd) and A(Bd)→ A(Amd) which are induced by isomorphisms between Artin groups of type B and centralizers of periodic braids. In this paper, we show that the monomorphisms A(Bd) → A(Amd−1), A(Bd) → A(Bmd) and A(Bd)→ A(Amd) induce injective functions on the set of conjugacy classes, and that none of the monomorphisms A(Bn)→ A(An), A(Ãn−1)→ A(Bn) and A(C̃n−1)→ A(Bn) does so.
منابع مشابه
On the type of conjugacy classes and the set of indices of maximal subgroups
Let $G$ be a finite group. By $MT(G)=(m_1,cdots,m_k)$ we denote the type of conjugacy classes of maximal subgroups of $G$, which implies that $G$ has exactly $k$ conjugacy classes of maximal subgroups and $m_1,ldots,m_k$ are the numbers of conjugates of maximal subgroups of $G$, where $m_1leqcdotsleq m_k$. In this paper, we give some new characterizations of finite groups by ...
متن کاملSome connections between powers of conjugacy classes and degrees of irreducible characters in solvable groups
Let $G$ be a finite group. We say that the derived covering number of $G$ is finite if and only if there exists a positive integer $n$ such that $C^n=G'$ for all non-central conjugacy classes $C$ of $G$. In this paper we characterize solvable groups $G$ in which the derived covering number is finite.
متن کاملGroups whose set of vanishing elements is exactly a conjugacy class
Let $G$ be a finite group. We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $chi$ of $G$ such that $chi(g)=0$. In this paper, we classify groups whose set of vanishing elements is exactly a conjugacy class.
متن کاملMorse Theory and Conjugacy Classes of Finite Subgroups
We construct a CAT(0) group containing a finitely presented subgroup with infinitely many conjugacy classes of finiteorder elements. Unlike previous examples (which were based on right-angled Artin groups) our ambient CAT(0) group does not contain any rank 3 free abelian subgroups. We also construct examples of groups of type Fn inside mapping class groups, Aut(Fk), and Out(Fk) which have infin...
متن کاملCOMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS
Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of...
متن کامل