Finite groups whose minimal subgroups are normal

doi:10.1007/BF01110184

Citations

PDF

Open Access

More filters

Journal Article•DOI•

On weakly s-permutable subgroups of finite groups

[...]

Alexander N. Skiba

01 Sep 2007-Journal of Algebra

TL;DR: In this article, the problem of weakly s-permutable subgroups in finite groups has been studied under the assumption that all subgroups H with |H | = |D | are weakly S-permutable in G.

...read moreread less

228 citations

Journal Article•DOI•

On minimal subgroups of finite groups

[...]

Adolfo Ballester-Bolinches¹, M. C. Pedraza-Aguilera¹•Institutions (1)

University of Valencia¹

01 Dec 1996-Acta Mathematica Hungarica

125 citations

Cites background from "Finite groups whose minimal subgrou..."

...Later Buckley [ 3 ] proved that if G is a group of odd order whose minimal subgroups are normal in G, then the group G is supersoluble....
[...]

Journal Article•DOI•

ON c-NORMAL MAXIMAL AND MINIMAL SUBGROUPS OF SYLOW SUBGROUPS OF FINITE GROUPS

[...]

Wei Huaquan

30 Apr 2001-Communications in Algebra

TL;DR: A subgroup H is called c-normal in G if there exists a normal subgroup N of G such that HN = G and H ∩ N ≤ HG = CoreG(H) as discussed by the authors.

...read moreread less

Abstract: A subgroup H is called c-normal in G if there exists a normal subgroup N of G such that HN = G and H ∩ N ≤ HG = CoreG(H). The purpose of this paper is to generalize some results obtained by some authors about supersolvable groups to a saturated formation containing the class of supersolvable groups.

...read moreread less

112 citations

Cites background from "Finite groups whose minimal subgrou..."

...And Buckley in [4] proved that a finite group G of odd order is supersolvable if all minimal subgroups of G are normal in G....
[...]

Journal Article•DOI•

C-supplemented subgroups of finite groups

[...]

Adolfo Ballester-Bolinches¹, Yanming Wang², Guo Xiuyun³•Institutions (3)

University of Valencia¹, Sun Yat-sen University², Shanxi University³

01 Sep 2000-Glasgow Mathematical Journal

TL;DR: A subgroup H of a group G is said to be c-supplemented in G if there exists a subgroup K of G such that HKa G and H\ K is contained in CoreGOHU.

...read moreread less

Abstract: A subgroup H of a group G is said to be c-supplemented in G if there exists a subgroup K of G such that HKa G and H\ K is contained in CoreGOHU .W e follow Hall's ideas to characterize the structure of the finite groups in which every subgroup is c-supplemented. Properties of c-supplemented subgroups are also applied to determine the structure of some finite groups.

...read moreread less

112 citations

Cites background from "Finite groups whose minimal subgrou..."

...1 (2) we know that G=N is c-complemented; hence G=N is supersolvable by induction....
[...]
...(2)(b) If p > 2, then the exponent of P is p....
[...]
...(2) G is a minimal non-nilpotent group so that G has the following properties....
[...]
...(2) Suppose that H=N is c-supplemented in G=N....
[...]
...(2)(a) There exists a normal Sylow p-subgroup of G such that G P --- Q....
[...]

Journal Article•DOI•

On the supersolvability of finite groups

[...]

Mohamed Asaad¹, Ayesha Shaalan¹•Institutions (1)

Cairo University¹

01 Oct 1989-Archiv der Mathematik

92 citations

Collapse

References

PDF

Open Access

More filters

Book•DOI•

Endliche Gruppen I

[...]

Bertram Huppert

01 Jan 1967

5,518 citations

Journal Article•DOI•

Finite groups in which the nonnormal subgroups have nontrivial intersection

[...]

Norman Blackburn

01 Jan 1966-Journal of Algebra

TL;DR: In this article, the authors give an example of such a group and obtain the non-Abelian Dedekind groups of order a power of 2 by taking -4 to be the direct product of a cyclic group of order 4 with an elementary Abelian group and ~2 to be a unique element of J which is a square.

...read moreread less

41 citations

"Finite groups whose minimal subgrou..." refers background in this paper

...Examples are Dedekind groups (finite groups in which every subgroup is normal) and a class of groups characterized by Blackburn [ 1 ]....
[...]

Journal Article•DOI•

Centralizers of abelian normal subgroups of p-groups

[...]

J. L. Alperin¹•Institutions (1)

University of Chicago¹

01 Jul 1964-Journal of Algebra

33 citations

Finite groups whose minimal subgroups are normal

Citations

Cites background from "Finite groups whose minimal subgrou..."

Cites background from "Finite groups whose minimal subgrou..."

Cites background from "Finite groups whose minimal subgrou..."

References

"Finite groups whose minimal subgrou..." refers background in this paper

Related Papers (5)