We enumerate Hurwitz orbits of shortest reflection factorizations an arbitrary element in the infinite family $G(m, p, n)$ complex groups. As a consequence, we characterize elements for which action is transitive and give simple criterion to tell when two belong same orbit. also quasi-Coxeter (those with factorization that generates whole group) n)$.

In this paper, we characterize spaces of L∞-functions on a compact Hausdorff space that are invariant under transitive and continuous group action. This work is analogous to established results concerning measurable functions space. The case for cannot be proved in the same way when endowed with norm-topology, but similar argument can used given weak*-topology, as show paper.

Until 1980, there was no such subgroup as ‘infinite permutation groups’, according to the Mathematics Subject Classification: permutation groups were assumed to be finite. There were a few papers, for example [10, 62], and a set of lecture notes by Wielandt [72], from the 1950s. Now, however, there are far more papers on the topic than can possibly be summarised in an article like this one. I s...

The extended modular group $\overline{\Gamma}$ is isomorphic to the amalgamated free product of two dihedral groups $D_2$ and $D_3$ with amalgamation $\mathbb{Z}_2$. This acts on rational numbers transitively. In this study, we obtain elements in that are mappings between given rationals. Also, express these as a word generators. We use interesting relations continued fractions Farey graph.

Verb is a word which shows action happening time, generally has subject and time known in verbs fact this quality makes deference between verb gerund. According to syntax, we have three types of – Transitive verb, intransitive Hukmi Motadi (Hukmi Transitive) verb. Most the two roots (present Past). structure, verbs: simple (as, root+suffix: ʣ+əm à ʣəm, χwr+əm χwrəm zə ɖoɖə́i χwrəm.) derivative a...

We show that various notions of local homogeneity for CR-manifolds are equivalent. In particular, if germs at any two points of a CR-manifold are CR-equivalent, there exists a transitive local Lie group action by CR-automorphisms near every point.

We compare three approaches to the notion of conjugacy for semigroups, the first one via the transitive closure of the uv ∼ vu relation, the second one via an action of inverse semigroups on themselves by partial transformations, and the third one via characters of finitedimensional representations.