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On zero-symmetric nearrings with identity whose additive groups are simple

Wen-Fong Ke, Johannes H. Meyer, Günter F. Pilz, Gerhard Wendt (2024)

Czechoslovak Mathematical Journal

We investigate conditions on an infinite simple group in order to construct a zero-symmetric nearring with identity on it. Using the Higman-Neumann-Neumann extensions and Clay’s characterization, we obtain zero-symmetric nearrings with identity with the additive groups infinite simple groups. We also show that no zero-symmetric nearring with identity can have the symmetric group Sym ( ℕ ) as its additive group.

On Π -property of some maximal subgroups of Sylow subgroups of finite groups

Zhengtian Qiu, Jianjun Liu, Guiyun Chen (2023)

Czechoslovak Mathematical Journal

Let H be a subgroup of a finite group G . We say that H satisfies the Π -property in G if for any chief factor L / K of G , | G / K : N G / K ( H K / K ∩ L / K ) | is a π ( H K / K ∩ L / K ) -number. We study the influence of some p -subgroups of G satisfying the Π -property on the structure of G , and generalize some known results.

On π-Groupoids

Zoran Stojaković, Janez Ušan (1979)

Publications de l'Institut Mathématique

On σ -permutably embedded subgroups of finite groups

Chenchen Cao, Li Zhang, Wenbin Guo (2019)

Czechoslovak Mathematical Journal

Let σ = { σ i : i ∈ I } be some partition of the set of all primes ℙ , G be a finite group and σ ( G ) = { σ i : σ i ∩ π ( G ) ≠ ∅ } . A set ℋ of subgroups of G is said to be a complete Hall σ -set of G if every non-identity member of ℋ is a Hall σ i -subgroup of G and ℋ contains exactly one Hall σ i -subgroup of G for every σ i ∈ σ ( G ) . G is said to be σ -full if G possesses a complete Hall σ -set. A subgroup H of G is σ -permutable in G if G possesses a complete Hall σ -set ℋ such that H A x = A x H for all A ∈ ℋ and all x ∈ G . A subgroup H of G is σ -permutably embedded in G if H is σ -full...

OnCSQ-normal subgroups of finite groups

Yong Xu, Xianhua Li (2016)

Open Mathematics

We introduce a new subgroup embedding property of finite groups called CSQ-normality of subgroups. Using this subgroup property, we determine the structure of finite groups with some CSQ-normal subgroups of Sylow subgroups. As an application of our results, some recent results are generalized.

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