Subgroups of the group E6(q) which are generated by root subgroups

Representations of the Alternating Group Which Are Irreducible over Subgroups

Normal Subgroups of the Modular Group Which Are Not Congruence Subgroups

A subgroup of V containing a principal congruence subgroup T(«) is said to be a congruence subgroup, and is of level « if « is the least such integer. In a recent article [2] the writer determined all normal subgroups of T of genus 1 (see [l] for the definition of the genus of a subgroup of r). An interesting question that arises is to decide which of these are also congruence subgroups. In thi...

On the norm of the derived‎ subgroups of all subgroups of a finite group

In this paper‎, ‎we give a complete proof of Theorem 4.1(ii) and a new‎ ‎elementary proof of Theorem 4.1(i) in [Li and Shen‎, ‎On the‎ ‎intersection of the normalizers of the derived subgroups of all‎ ‎subgroups of a finite group‎, ‎ J‎. ‎Algebra, ‎323  (2010) 1349--1357]‎. ‎In addition‎, ‎we also give a generalization of Baer's Theorem‎.

The Modular Group A Finitely Generated Group with Interesting Subgroups

The action of Möbius transformations with real coefficients preserves the hyperbolic metric in the upper half-plane model of the hyperbolic plane. The modular group is an interesting group of hyperbolic isometries generated by two Möbius transformations, namely, an order-two element, g2 HzL = -1 ê z, and an element of infinite order, g• HzL = z + 1. Viewing the action of the group elements on a...

On Normal Subgroups Which Are Direct Products

Now that the classification of finite simple groups is complete, it is logical to look at the extension problem. An important special case to consider is when M is a minimal normal subgroup of G and both G/M and M are known groups. If M is abelian, various techniques have been used to derive information about G. Indeed, almost the entire theory of finite solvable groups can be said to rest upon...