Maximal finite subgroups and minimal classes
نویسندگان
چکیده
We apply Voronoi’s algorithm to compute representatives of the conjugacy classes of maximal finite subgroups of the unit group of a maximal order in some simple Q-algebra. This may be used to show in small cases that non-conjugate orders have non-isomorphic unit groups.
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 کاملMaximal finite subgroups and minimal classes by Renaud COULANGEON and Gabriele NEBE
We apply Voronoi’s algorithm to compute representatives of the conjugacy classes of maximal finite subgroups of the unit group of a maximal order in some simple Q -algebra. This may be used to show in small cases that non-conjugate orders have non-isomorphic unit groups.
متن کاملTriple factorization of non-abelian groups by two maximal subgroups
The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...
متن کاملComputing maximal subgroups of finite groups
We describe a practical algorithm for computing representatives of the conjugacy classes of maximal subgroups in a finite group, together with details of its implementation for permutation groups in the MAGMA system. We also describe methods for computing complements of normal subgroups and minimal supplements of normal soluble subgroups of finite groups.
متن کاملMaximal complements in finite groups
Let G be a finite group with a non-abelian minimal normal subgroup N which is a direct product of the simple group X. The maximal subgroups of G which complement N and their conjugacy classes are parametrised in terms of certain homomorphisms taking values in AutX and satisfying particular conditions.
متن کامل