A transitively normal subgroup of a group G is one that is normal in every subgroup in which it is subnormal. This concept is obviously related to the transitivity of normality because the latter holds in every subgroup of a group G if and only if every subgroup of G is transitively normal. In this paper we describe the structure of a group whose cyclic subgroups (or a part of them) are transit...

By refining an idea of Farrell, we present a sufficient condition in terms the Jiang subgroup for vanishing signature and Hirzebruch's $\chi_y$-genus on compact smooth K\"{a}hler manifolds respectively. Along this line show that non-positively curved manifold vanishes when center its fundamental group is non-trivial, which partially answers question Farrell. Moreover, latter case all Chern numb...

This paper is a continuation of our previous work with Margalit where we studied group actions on projection complexes. In that paper, demonstrated sufficient conditions so the normal closure family subgroups vertex stabilizers free product certain conjugates these subgroups. this study both quotient complex by subgroup and action complex. We show under $\\delta$-hyperbolic. Additionally, circu...

1 Multiply transitive groups Theorem 1.1. Let Ω be a finite set and G ≤ Sym(Ω) be 2–transitive. Let N E G be a minimal normal subgroup. Then one of the following holds: (a) N is regular and elementary abelian. (b) N is primitive, simple and not abelian. Proof. First we show that N is unique. Suppose that M is another minimal normal subgroup of G, so N ∩M = {e} and therefore [N,M ] = {e}. Since ...