All known finite sharply 4-transitive permutation sets containing the identity are groups, namely S4, S5, A6 and the Mathieu group of degree 11. We prove that a sharply 4-transitive permutation set on 11 elements containing the identity must necessarily be the Mathieu group of degree 11. The proof uses direct counting arguments. It is based on a combinatorial property of the involutions in the ...

Let L2 denote the stable homotopy category of v−1 2 BP -local spectra at the prime three. In [2], it is shown that the Picard group of L2 consisting of isomorphic classes of invertible spectra is isomorphic to either the direct sum of Z and Z/3 or the direct sum of Z and two copies of Z/3. In this paper, we conclude the Picard group is isomorphic to the latter group by showing the existence of ...

Non-invertible discrete-time dynamical systems can be derived from group actions. In the present work possibility of application of this method to systems of ordinary differential equations is studied. Invertible group actions are considered as possible candidates for stroboscopic maps of ordinary differential equations. It is shown that a map on SU (2) group interpolates exactly a flow of the ...

We show that if T is an isometry (as metric spaces) from an open subgroup of the group of the invertible elements in a unital semisimple commutative Banach algebra onto an open subgroup of the group of the invertible elements in a unital Banach algebra, then T (1)T is an isometrical group isomorphism. In particular, T (1)T is extended to an isometrical real algebra isomorphism from A onto B.

‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

Definition 3.4. The ideal group IA of a noetherian domain A is the group of invertible fractional ideals. Note that, despite the name, elements of IA need not be ideals. Every nonzero principal fractional ideal (x) is invertible (since (x)−1 = (x−1)), and a product of principal fractional ideals is principal (since (x)(y) = (xy)), as is the unit ideal (1), thus the set of nonzero principal frac...

Let A be a unital C -algebra with involution represented in a Hilbert space H, G the group of invertible elements of A, U the unitary group of A, G the set of invertible selfadjoint elements of A, Q = f" 2 G : " = 1g the space of re ections and P = Q \ U . For any positive a 2 G consider the a-unitary group Ua = fg 2 G : a g a = g g, i.e., the elements which are unitary with respect to the scal...

We study invertible generating pairs of fundamental groups of graph manifolds, that is, pairs of elements (g, h) for which the map g → g −1 , h → h −1 extends to an automorphism. We show in particular that a graph manifold is of Heegaard genus 2 if and only if its fundamental group has an invertible generating pair.

An MI-group is an algebraic structure based on a generalization of the concept of a monoid that satisfies the cancellation laws and is endowed with an invertible anti-automorphism representing inversion. In this paper, a topology is defined on an MI-group $G$ under which $G$ is  a topological MI-group. Then we will identify open, discrete and compact MI-subgroups. The connected components of th...

Let A be a complex unital Banach algebra with unit 1. The sets of all invertible and quasinilpotent elements (σ(a) = {0}) of A will be denoted by A and A, respectively. The group inverse of a ∈ A is the unique element a ∈ A which satisfies aaa = a, aaa = a, aa = aa. If the group inverse of a exists, a is group invertible. Denote by A the set of all group invertible elements of A. The generalize...