Search results for "Locally finite group"
showing 10 items of 52 documents
On two classes of finite supersoluble groups
2017
ABSTRACTLet ℨ be a complete set of Sylow subgroups of a finite group G, that is, a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A subgroup H of G is called ℨ-S-semipermutable if H permutes with every Sylow p-subgroup of G in ℨ for all p∉π(H); H is said to be ℨ-S-seminormal if it is normalized by every Sylow p-subgroup of G in ℨ for all p∉π(H). The main aim of this paper is to characterize the ℨ-MS-groups, or groups G in which the maximal subgroups of every Sylow subgroup in ℨ are ℨ-S-semipermutable in G and the ℨ-MSN-groups, or groups in which the maximal subgroups of every Sylow subgroup in ℨ are ℨ-S-seminormal in G.
On finite groups with many supersoluble subgroups
2017
[EN] The solubility of a finite group with less than 6 non-supersoluble subgroups is confirmed in the paper. Moreover we prove that a finite insoluble group has exactly 6 non-supersoluble subgroups if and only if it is isomorphic to A5 or SL2 (5). Furthermore, it is shown that a finite insoluble group has exactly 22 non-nilpotent subgroups if and only if it is isomorphic to A5 or SL2 (5). This confirms a conjecture of Zarrin (Arch Math (Basel) 99:201 206, 2012).
Maximal subgroups and PST-groups
2013
A subgroup H of a group G is said r to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maxmial subgroups, Arch. Math. (Basel), 2011, 96(1), 19-25)] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions o…
Some results on locally finite groups
2017
En esta tesis se presentan algunos resultados sobre p-nilpotencia y permutabilidad en grupos localmente finitos. Está estructurada en cinco capítulos. El primer capítulo, que tiene carácter introductorio: contiene definiciones y resultados conocidos que serán utilizados en los capítulos sucesivos. Por tratarse de resultados ya conocidos, se introducen con referencias y sin demostraciones. En el capítulo 2 se trata la p-nilpotencia en grupos hiperfinitos, donde p es un primo. Los resultados presentados se encuentran publicados en el siguiente artículo: Ballester-Bolinches, A.; Camp-Mora, S.; Spagnuolo, F., "On p-nilpotency of hyperfinite groups". Monatshefte f¨ur Mathematik, 176, no. 4, 497–…
Pronormal subgroups of a direct product of groups
2009
[EN] We give criteria to characterize abnormal, pronormal and locally pronormal subgroups of a direct product of two finite groups A×B, under hypotheses of solvability for at least one of the factors, either A or B.
On generalised subnormal subgroups of finite groups
2013
Let be a formation of finite groups. A subgroup M of a finite group G is said to be -normal in G if belongs to . A subgroup U of a finite group G is called a K--subnormal subgroup of G if either U = G or there exist subgroups U = U0 ≤ U1 ≤ … ≤ Un = G such that Ui − 1 is either normal or -normal in Ui, for i = 1, 2, …, n. The K--subnormality could be regarded as the natural extension of the subnormality to formation theory and plays an important role in the structural study of finite groups. The main purpose of this paper is to analyse classes of finite groups whose K--subnormal subgroups are exactly the subnormal ones. Some interesting extensions of well-known classes of groups emerge.
Confined subgroups in periodic simple finitary linear groups
2002
A subgroupX of the locally finite groupG is said to beconfined, if there exists a finite subgroupF≤G such thatX g∩F≠1 for allg∈G. Since there seems to be a certain correspondence between proper confined subgroups inG and non-trivial ideals in the complex group algebra ℂG, we determine the confined subgroups of periodic simple finitary linear groups in this paper.
Products of locally dihedral subgroups
2012
AbstractIt is shown that a group G=AB which is a product of two periodic locally dihedral subgroups A and B is soluble.
Hyper-abelian groups with finite co-central rank
2004
AbstractA group G has finite co-central rank s if there exists a least non-negative integer s such that every finitely generated subgroup H can be generated by at most s elements modulo the centre of H. The investigation of such groups has been started in [J.P. Sysak, A. Tresch, J. Group Theory 4 (2001) 325]. It is proved that hyper-abelian groups with finite co-central rank are locally soluble. The interplay between the Prüfer rank condition, the condition of having finite abelian section rank and the finite co-central rank condition is studied. As one result, a hyper-abelian group G with finite co-central rank has an ascending series with abelian factors of finite rank and every chief fac…
The Jordan-Hölder theorem and prefrattini subgroups of finite groups
1995
by A. BALLESTER-BOLINCHES and L. M. EZQUERRO(Received 26 January, 1994)Introduction. All groups considered are finite. In recent years a number ofgeneralizations of the classic Jordan-Holder Theorem have been obtained (see [7],Theorem A.9.13): in a finite group G a one-to-one correspondence as in the Jordan-Holder Theorem can be defined preserving not only G-isomorphic chief factors but eventheir property of being Frattini or non-Frattini chief factors. In [2] and [13] a newdirection of generalization is presented: the above correspondence can be defined in sucha way that the corresponding non-Frattini chief factors have the same complement(supplement).In this paper we present a necessary a…