# New Types of Transitive Functions and Minimal Systems

**Tags:** MULTIPLY transitive groups; FINITE groups; PERMUTATION groups; FINITE simple groups; GROUP theory; FC-groups

## Related Articles

- On ?-Supplemented Minimal Subgroups of Finite Groups. Xianggui Zhong; Shirong Li // Southeast Asian Bulletin of Mathematics;2004, Vol. 28 Issue 6, p1141
Let G be a finite group. A subgroup H is called c-supplemented in G if there exists a subgroup K of G such that HK = G and H n K = HG, where HG =: CoreG(H) = ng?GHg. We obtain some results on the relationship between the c-supplemented condition of minimal subgroup of G and the structure of G....

- BARELY TRANSITIVE LOCALLY NILPOTENT P-GROUPS. ASAR, A. O. // Journal of the London Mathematical Society;04/01/1997, Vol. 55 Issue 2, p357
B. Hartley in [4] introduced the class of barely transitive groups. By definition, a group of permutations G on an infinite set X is called barely transitive if G itself is transitive on X while every orbit of every proper subgroup of G is finite. If G is locally finite and G2`G then the theorem...

- ON WREATH PRODUCT OF PERMUTATION GROUPS. A. A., IBRAHIM; M. S., AUDU // Proyecciones - Journal of Mathematics;2007, Vol. 26 Issue 1, p73
This report is essentially an upgrade of the results of Audu (see [1] and [2]) on some finite permutation groups. It consists of the basic procedure for computing wreath product of groups. We also discussed the conditions under which the wreath products of permutation groups are faithful,...

- On the solvability of a group with permutable subgroups. Monakhov, V. // Mathematical Notes;Mar2013, Vol. 93 Issue 3/4, p460
The solvability of a finite group G = AB is established under the assumption that the subgroups A and B are solvable and the Carter subgroups of A commute with the Carter subgroups of B.

- A solution of Wielandt's problem for the sporadic groups. Ch, Manzaeva N. // Sibirskie Elektronnye Matematicheskie Izvestiia;2012, Vol. 9, p294
Let Ï€ be a set of primes. A finite group G is a DÏ€-group if all maximal Ï€-subgroups of G are conjugate. In 1979 H. Wielandt posed the following problem: in which finite simple groups every subgroup is a DÏ€-group? We solve this problem for the sporadic groups.

- Finite Groups with S-Semipermutable Subgroups. Peichen Zhao // Advances in Information Sciences & Service Sciences;May2012, Vol. 4 Issue 8, p61
A subgroup of a group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of G . A subgroup H of a group G is said to be S-Semipermutable in G if H is permutable with every Sylow p-subgroup S of G with (p, |G|)=1. In this paper we investigate the infulence of...

- Normalizers of the Sylow 2-Subgroups in Finite Simple Groups. Kondrat'ev, A. S. // Mathematical Notes;Sep/Oct2005, Vol. 78 Issue 3/4, p338
The description of the normalizers of the Sylow 2-subgroups in finite simple groups is completed.

- Transitive Permutation Representation For Symmetrically Generated Groups. Sayed, Mohamed // Southeast Asian Bulletin of Mathematics;2005, Vol. 29 Issue 1, p157
This paper introduces a new idea for presenting certain transitive extentions of a given transitive permutation group. A group is given as homomorphic image of an infinite semi-direct product of free products of n copies of cyclic groups of order 2 by a group of automorphisms.

- GROUP LAWS AND FREE SUBGROUPS IN TOPOLOGICAL GROUPS. MIKLS ABRT // Bulletin of the London Mathematical Society;Aug2005, Vol. 37 Issue 4, p525
A proof is given that a permutation group in which different finite sets have different stabilizers cannot satisfy any group law. For locally compact topological groups with this property, almost all finite subsets of the group are shown to generate free subgroups. Consequences of these theorems...