All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 8 Next

Displaying 141 – 160 of 249

Showing per page

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...

Prime divisors of conjugacy class lengths in finite groups

Carlo Casolo (1991)

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

We show that in a finite group G which is p -nilpotent for at most one prime dividing its order, there exists an element whose conjugacy class length is divisible by more than half of the primes dividing G / Z ⁢ G .

Some results on Sylow numbers of finite groups

Yang Liu, Jinjie Zhang (2024)

Czechoslovak Mathematical Journal

We study the group structure in terms of the number of Sylow p -subgroups, which is denoted by n p ( G ) . The first part is on the group structure of finite group G such that n p ( G ) = n p ( G / N ) , where N is a normal subgroup of G . The second part is on the average Sylow number asn ( G ) and we prove that if G is a finite nonsolvable group with asn ( G ) < 39 / 4 and asn ( G ) ≠ 29 / 4 , then G / F ( G ) ≅ A 5 , where F ( G ) is the Fitting subgroup of G . In the third part, we study the nonsolvable group with small sum of Sylow numbers.

Currently displaying 141 – 160 of 249