Abstract We consider a finite, connected and simple graph Γ that admits vertex-transitive group of automorphisms

The only finite nonabelian simple group acting on a homology 3-sphere necessarily non-freely is the dodecahedral group A5 ∼= PSL(2, 5) (in analogy, the only finite perfect group acting freely on a homology 3-sphere is the binary dodecahedral group A∗5 ∼= SL(2, 5)). In the present paper we show that the only finite simple groups acting on a homology 4-sphere, and in particular on the 4-sphere, a...

We prove that a finite group with nilpotent subgroup H and H-connected transversals is solvable. The proof depends on the classification of finite simple groups.

Introduction. Zilber’s original trichotomy conjecture proposed an explicit classification of all one-dimensional objects arising in model theory. At one point, classifying the simple groups of finite Morley rank was viewed as a subproblem whose affirmative answer would justify this conjecture. Zilber’s conjecture was eventually refuted by Hrushovski [9], and the classification of simple groups ...

Suppose G is an almost simple group containing a subgroup isomorphic to the three-dimensional Heisenberg group. For example any finite index subgroup of SL(3, Z) is such a group. The main result of this paper is that every action of G on a closed oriented surface by area preserving diffeomorphisms factors through a finite group.

We find all the inequivalent simple root systems for the complex reflection groups G12, G24, G25 and G26. Then we give all the non-congruent essential presentations of these groups by generators and relations. The methed used in the paper is applicable to any finite (complex) reflection groups. Introduction. Shephard and Todd classified all the finite complex reflection groups in paper [5]. Lat...

Abstract In this paper we apply social epistemology to mathematical proofs and their role in knowledge. The most famous modern collaborative proof effort is the Classification of Finite Simple Groups . history sociology have been well-documented by Alma Steingart (2012), who highlights a number surprising unusual features endeavour that set it apart from smaller-scale pieces mathematics. These ...