this paper gives a short survey of some of the known results generalizing the theorem, credited to i. schur, that if the central factor group is finite then the derived subgroup is also finite.

In [15], Kaplansky introduced Baer rings as rings in which every right (left) annihilator ideal is generated by an idempotent. According to Clark [9], a ring R is called quasi-Baer if the right annihilator of every right ideal is generated (as a right ideal) by an idempotent. Further works on quasi-Baer rings appear in [4, 6, 17]. Recently, Birkenmeier et al. [8] called a ring R to be a right (...

In the paper we prove (modulo classification of finite simple groups) an analogue famous Baer-Suzuki theorem for π-radical a group, where π is set primes.

In [6], the compatibility of Baer involutions and elations was studied. Further compatibility results for translation planes of dimension 2 were obtained in [10]. For example [6, Theorem (2.2)], we have the following. Let n be a derivable translation plane of even order q, q # 2, with derivable net N. Let EL denote an elation group in the translation complement which fixes the component L of N ...

In this paper‎, ‎we first present some properties of lower and upper central series of pair of groups‎. ‎Then the notion of $n$-isoclinism for the classification of pairs of groups is introduced‎, ‎and some of the structural properties of the created classes are proved‎. ‎Moreover some interesting theorems such as Baer Theorem‎, ‎Bioch Theorem‎, ‎Hirsh Theorem for pair of groups are generalized...