Finite groups with a 2-Sylow subgroup containing a self-centralizing elementary Abelian subgroup of order 8

1974 ◽  
Vol 16 (6) ◽  
pp. 1133-1136
Author(s):  
V. M. Sitnikov
Keyword(s):  
Finite Groups ◽  
Sylow Subgroup ◽  
Abelian Subgroup ◽  
Elementary Abelian Subgroup

Finite groups in which a Sylow two-subgroup contains an elementary abelian subgroup of index 4

1977 ◽  
Vol 16 (5) ◽  
pp. 375-387 ◽  
Author(s):  
A. S. Kondrat'ev
Keyword(s):  
Finite Groups ◽  
Abelian Subgroup ◽  
Elementary Abelian Subgroup

scholarly journals On infinite groups in which all abelian subgroups are locally cyclic

2021 ◽  
Author(s):  
Costantino Delizia ◽  
Chiara Nicotera
Keyword(s):  
Finite Groups ◽  
Abelian Subgroup ◽  
Periodic Case ◽  
Infinite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Periodic Groups ◽  
Abelian Subgroups

AbstractThe structure of locally soluble periodic groups in which every abelian subgroup is locally cyclic was described over 20 years ago. We complete the aforementioned characterization by dealing with the non-periodic case. We also describe the structure of locally finite groups in which all abelian subgroups are locally cyclic.

Finite Groups with Some Subgroups of Sylow Subgroups s∗-Semipermutable

2021 ◽  
Vol 58 (2) ◽  
pp. 147-156
Author(s):  
Qingjun Kong ◽  
Xiuyun Guo
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sylow Subgroup ◽  
Subnormal Subgroup ◽  
Sylow Subgroups ◽  
A Finite Group

We introduce a new subgroup embedding property in a finite group called s∗-semipermutability. Suppose that G is a finite group and H is a subgroup of G. H is said to be s∗-semipermutable in G if there exists a subnormal subgroup K of G such that G = HK and H ∩ K is s-semipermutable in G. We fix in every non-cyclic Sylow subgroup P of G some subgroup D satisfying 1 < |D| < |P | and study the structure of G under the assumption that every subgroup H of P with |H | = |D| is s∗-semipermutable in G. Some recent results are generalized and unified.

FINITE GROUPS WITH GIVEN NEARLY S-QUASINORMAL SUBGROUPS

2008 ◽  
Vol 01 (03) ◽  
pp. 369-382
Author(s):  
Nataliya V. Hutsko ◽  
Vladimir O. Lukyanenko ◽  
Alexander N. Skiba
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Finite Groups ◽  
Sylow Subgroup ◽  
Cyclic Subgroup ◽  
Saturated Formation ◽  
Supersoluble Groups ◽  
Sylow Subgroups ◽  
Quasinormal Subgroup ◽  
A Finite Group

Let G be a finite group and H a subgroup of G. Then H is said to be S-quasinormal in G if HP = PH for all Sylow subgroups P of G. Let HsG be the subgroup of H generated by all those subgroups of H which are S-quasinormal in G. Then we say that H is nearly S-quasinormal in G if G has an S-quasinormal subgroup T such that HT = G and T ∩ H ≤ HsG. Our main result here is the following theorem. Let [Formula: see text] be a saturated formation containing all supersoluble groups and G a group with a normal subgroup E such that [Formula: see text]. Suppose that every non-cyclic Sylow subgroup P of E has a subgroup D such that 1 < |D| < |P| and all subgroups H of P with order |H| = |D| and every cyclic subgroup of P with order 4 (if |D| = 2 and P is a non-abelian 2-group) having no supersoluble supplement in G are nearly S-quasinormal in G. Then [Formula: see text].

Finite Groups with Normal Normalizers

1968 ◽  
Vol 20 ◽  
pp. 1256-1260 ◽  
Author(s):  
C. Hobby
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sylow Subgroup ◽  
A Finite Group

We say that a finite group G has property N if the normalizer of every subgroup of G is normal in G. Such groups are nilpotent since every Sylow subgroup is normal (the normalizer of a Sylow subgroup is its own normalizer). Thus it is sufficient to study p-groups which have property N. Note that property N is inherited by subgroups and factor groups.

FINITE GROUPS WITH MULTIPLICITY-FREE PERMUTATION CHARACTERS

2005 ◽  
Vol 04 (02) ◽  
pp. 187-194
Author(s):  
MICHITAKU FUMA ◽  
YASUSHI NINOMIYA
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Abelian Subgroup ◽  
Hecke Algebra ◽  
Endomorphism Algebra ◽  
Theoretic Method ◽  
A Finite Group ◽  
Multiplicity Free ◽  
Canonical Involution

Let G be a finite group and H a subgroup of G. The Hecke algebra ℋ(G,H) associated with G and H is defined by the endomorphism algebra End ℂ[G]((ℂH)G), where ℂH is the trivial ℂ[H]-module and (ℂH)G = ℂH⊗ℂ[H] ℂ[G]. As is well known, ℋ(G,H) is a semisimple ℂ-algebra and it is commutative if and only if (ℂH)G is multiplicity-free. In [6], by a ring theoretic method, it is shown that if the canonical involution of ℋ(G,H) is the identity then ℋ(G,H) is commutative and, if there exists an abelian subgroup A of G such that G = AH then ℋ(G,H) is commutative. In this paper, by a character theoretic method, we consider the commutativity of ℋ(G,H).

Finite groups with each non-normal subgroup having maximal normal cores

2016 ◽  
Vol 15 (03) ◽  
pp. 1650053
Author(s):  
Heng Lv ◽  
Zhibo Shao ◽  
Wei Zhou
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Finite Groups ◽  
Abelian Subgroup ◽  
A Finite Group

In this paper, we study a finite group [Formula: see text] such that [Formula: see text] is a prime for each non-normal subgroup [Formula: see text] of [Formula: see text]. We prove that such a group must contain a big abelian subgroup. More specifically, if such a group [Formula: see text] is not supersoluble, then there is an abelian subgroup [Formula: see text] such that [Formula: see text], and if [Formula: see text] is supersoluble, then there is an abelian subgroup [Formula: see text] such that [Formula: see text] or [Formula: see text], where [Formula: see text] and [Formula: see text] are primes.

scholarly journals Finite Groups with Minimal CSS-subgroups

2021 ◽  
Vol 14 (3) ◽  
pp. 1002-1014
Author(s):  
A. A. Heliel ◽  
R. A. Hijazi ◽  
S. M. Al-Shammari
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Finite Groups ◽  
Sylow Subgroup ◽  
Group A ◽  
A Finite Group

Let G be a finite group. A subgroup H of G is called SS-quasinormal in G if there is a supplement B of H to G such that H permutes with every Sylow subgroup of B. A subgroup H of G is called CSS-subgroup in G if there exists a normal subgroup K of G such that G = HK and H ∩K is SS-quasinormal in G. In this paper, we investigate the influence of minimal CSS-subgroups of G on its structure. Our results improve and generalize several recent results in the literature.

scholarly journals On finite groups containing a CCT-subgroup with a cyclic Sylow subgroup

1968 ◽  
Vol 25 (3) ◽  
pp. 523-531 ◽  
Author(s):  
Marcel Herzog
Keyword(s):  
Finite Groups ◽  
Sylow Subgroup
Sign in / Sign up

Export Citation Format

Share Document