Communications in Algebra

Gao, Yaxin; Li, Xianhua

doi: 10.1080/00927872.2024.2431159pmid: N/A

Abstract A subgroup S of a finite group G is called a p-sylowizer of a p-subgroup R in G if S is maximal in G with respect to having R as its Sylow p-subgroup. In this paper, we investigate p F -hypercentrally embedded structure of finite groups by using p-sylowizers of some p-subgroups with fixed order.

Li, Jinbao; Xu, Xia; Xu, Yuchen; Yang, Yong

doi: 10.1080/00927872.2024.2431641pmid: N/A

Abstract In this paper, we partially answer a question of Wujie Shi about the width of the order of the elements of a finite group.

Wu, Kaixun; Kang, Wangqiang; Pang, Linna; Lu, Jiakuan

doi: 10.1080/00927872.2024.2431887pmid: N/A

Abstract Let G be a finite group, and let p be a prime. In this paper, we obtain some conditions for G to be p-nilpotent or p-closed in terms of strongly monolithic characters.

Macedo Ferreira, Bruno Leonardo; Julius, Hayden

doi: 10.1080/00927872.2024.2431889pmid: N/A

Abstract– In this paper, we study additive maps f : A → A on an alternative Cayley-Dickson algebra A satisfying the product preserving property: f ( x ) f ( y ) = m whenever xy = k, where k and m are constant elements of A . We prove that f may be written as a multiple of a Jordan homomorphism. Unlike in the associative case, Jordan homomorphisms of strictly alternative division rings need not be homomorphisms or anti-homomorphisms, but we provide necessary and sufficient conditions for this to occur. We then extend these ideas to split alternative Cayley-Dickson algebras of characteristic not 2 and present some open questions when k or m is noninvertible. The final section handles the problem k = m = 0 and generalizes to biadditive maps that preserve the zero product.

Savin, Diana

doi: 10.1080/00927872.2024.2448237pmid: N/A

Abstract Let p 1, p 2 be two distinct prime integers, let n be a positive integer, n ≥ 3 and let ξn be a primitive root of order n of the unity. In the 3rd section of this paper we obtain a complete characterization for a quaternion algebra H ( p 1 , p 2 ) to be a division algebra over the nth cyclotomic field Q ( ξ n ) , when n ∈ { 3 , 4 , 6 , 7 , 8 , 9 , 11 , 12 } and we also obtain a characterization for a quaternion algebra H ( p 1 , p 2 ) to be a division algebra over the nth cyclotomic field Q ( ξ n ) , when n ∈ { 5 , 10 } . In the 4th section we obtain a complete characterization for a quaternion algebra H Q ( ξ n ) ( p 1 , p 2 ) to be a division algebra, when n = l k , with l a prime integer, l ≡ 3 (mod 4) and k a positive integer. In the last section of this article we obtain a complete characterization for a quaternion algebra H Q ( ξ l ) ( p 1 , p 2 ) to be a division algebra, when l is a Fermat prime number.

Pal, Sourav; Singh, Ravinder

doi: 10.1080/00927872.2024.2433081pmid: N/A

Abstract Klawa proved that global perinormality is preserved in a pullback construction which encompasses a classical D + M construction (Klawa H. (2023). Global perinormality in a generalized D + M construction. Communications in Algebra, 51:3015–3019). More precisely, if ( T , M ) is a local domain, with the residue field k, and an integral domain D whose quotient field is k, Klawa proved that if the pullback D × k T is globally perinormal, then D and T are also globally perinormal. We generalize this result by dropping the localness assumption from T. Several additional results, which are of independent interest, are also proved.

Yao, Lulu; Yu, Yalong

doi: 10.1080/00927872.2024.2433682pmid: N/A

Abstract Let K be a field, L a Lie algebra over K . A 2-Local derivation on L is a map (not linear in general) Δ : L → L which satisfies that for every x , y ∈ L , there exists a derivation D x , y (depending on x, y) on L such that Δ ( x ) = D x , y ( x ) and Δ ( y ) = D x , y ( y ) . In this article, we prove that any 2-local derivation of the n-th Schrödinger algebra s c h n is a derivation.

Hua, Peice; Li, Cai Heng; Zhang, Jia Ben; Zhou, Hui

doi: 10.1080/00927872.2024.2433686pmid: N/A

Abstract In this paper, we give a characterization of finite non-solvable groups which act flag-regularly on maps with negative square-free Euler characteristic. We also construct some interesting families of regular maps.

Betti, Barbara; Moscariello, Alessio; Romeo, Francesco; Singh, Jyoti

doi: 10.1080/00927872.2024.2434666pmid: N/A

Abstract In this paper, by using a combinatorial approach, we establish a new upper bound for the F-threshold c m ( m ) of determinantal rings generated by maximal minors. We prove that c m ( m ) coincides with the negative a-invariant in the case of 3 × n and 4 × n matrices and we conjecture such equality holds for all matrices.

Gorshkov, Ilya B.; Shao, Changguo; Mudziiri Shumba, Tendai M.

doi: 10.1080/00927872.2024.2436012pmid: N/A

Abstract Let N(G) be the set of sizes of the conjugacy classes of G, and let Ω be a set of relatively prime integers. We prove that if N ( G ) = ∏ n ∈ Ω { 1 , n } , then G ≃ A × ∏ P i where A is an abelian group, Pi is a Sylow pi -subgroup.