Displaying similar documents to “Connected transversals -- the Zassenhaus case”

On TI-subgroups and QTI-subgroups of finite groups

Ruifang Chen, Xianhe Zhao (2020)

Czechoslovak Mathematical Journal

Similarity:

Let G be a group. A subgroup H of G is called a TI-subgroup if H H g = 1 or H for every g G and H is called a QTI-subgroup if C G ( x ) N G ( H ) for any 1 x H . In this paper, a finite group in which every nonabelian maximal is a TI-subgroup (QTI-subgroup) is characterized.

Finite groups with some SS-supplemented subgroups

Mengling Jiang, Jianjun Liu (2021)

Czechoslovak Mathematical Journal

Similarity:

A subgroup H of a finite group G is said to be SS-supplemented in G if there exists a subgroup K of G such that G = H K and H K is S-quasinormal in K . We analyze how certain properties of SS-supplemented subgroups influence the structure of finite groups. Our results improve and generalize several recent results.

On weakly-supplemented subgroups of finite groups

Qingjun Kong (2019)

Czechoslovak Mathematical Journal

Similarity:

A subgroup H of a finite group G is weakly-supplemented in G if there exists a proper subgroup K of G such that G = H K . In this paper, some interesting results with weakly-supplemented minimal subgroups to a smaller subgroup of G are obtained.

Every 2 -group with all subgroups normal-by-finite is locally finite

Enrico Jabara (2018)

Czechoslovak Mathematical Journal

Similarity:

A group G has all of its subgroups normal-by-finite if H / H G is finite for all subgroups H of G . The Tarski-groups provide examples of p -groups ( p a “large” prime) of nonlocally finite groups in which every subgroup is normal-by-finite. The aim of this paper is to prove that a 2 -group with every subgroup normal-by-finite is locally finite. We also prove that if | H / H G | 2 for every subgroup H of G , then G contains an Abelian subgroup of index at most 8 .

Isolated subgroups of finite abelian groups

Marius Tărnăuceanu (2022)

Czechoslovak Mathematical Journal

Similarity:

We say that a subgroup H is isolated in a group G if for every x G we have either x H or x H = 1 . We describe the set of isolated subgroups of a finite abelian group. The technique used is based on an interesting connection between isolated subgroups and the function sum of element orders of a finite group.

On quotients of the space of orderings of the field ℚ(x)

Paweł Gładki, Bill Jacob (2016)

Banach Center Publications

Similarity:

In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings ( X ( x ) , G ( x ) ) - it is, in general, nontrivial to determine whether, for a subgroup G G ( x ) the derived quotient structure ( X ( x ) | G , G ) is a space of orderings, and we provide some insights into this problem. In particular, we show that if a quotient structure arising from a subgroup of index 2 is a space of orderings, then it necessarily is a profinite one.

Ulm-Kaplansky invariants of S(KG)/G

P. V. Danchev (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

Let G be an infinite abelian p-group and let K be a field of the first kind with respect to p of characteristic different from p such that s p ( K ) = or s p ( K ) = 0 . The main result of the paper is the computation of the Ulm-Kaplansky functions of the factor group S(KG)/G of the normalized Sylow p-subgroup S(KG) in the group ring KG modulo G. We also characterize the basic subgroups of S(KG)/G by proving that they are isomorphic to S(KB)/B, where B is a basic subgroup of G.

A note on weakly-supplemented subgroups and the solvability of finite groups

Xin Liang, Baiyan Xu (2022)

Czechoslovak Mathematical Journal

Similarity:

Suppose that G is a finite group and H is a subgroup of G . The subgroup H is said to be weakly-supplemented in G if there exists a proper subgroup K of G such that G = H K . In this note, by using the weakly-supplemented subgroups, we point out several mistakes in the proof of Theorem 1.2 of Q. Zhou (2019) and give a counterexample.

The superfocal subgroup

Marian Deaconescu (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

Nel presente lavoro vengono dimostrati teoremi d'esistenza di p -complementi normali nei gruppi finiti.

A characterization of the linear groups L 2 ( p )

Alireza Khalili Asboei, Ali Iranmanesh (2014)

Czechoslovak Mathematical Journal

Similarity:

Let G be a finite group and π e ( G ) be the set of element orders of G . Let k π e ( G ) and m k be the number of elements of order k in G . Set nse ( G ) : = { m k : k π e ( G ) } . In fact nse ( G ) is the set of sizes of elements with the same order in G . In this paper, by nse ( G ) and order, we give a new characterization of finite projective special linear groups L 2 ( p ) over a field with p elements, where p is prime. We prove the following theorem: If G is a group such that | G | = | L 2 ( p ) | and nse ( G ) consists of 1 , p 2 - 1 , p ( p + ϵ ) / 2 and some numbers divisible by 2 p , where p is a prime...