Authors:Qinhai Zhang Pages: 1 - 8 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 1-8, March 2019. Finite p-groups whose subgroups of given order are isomorphic and minimal non-abelian are classified. In addition, two results on a chain condition of ð’œt-groups are improved. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:39Z DOI: 10.1142/S1005386719000026

Authors:Janusz Konieczny Pages: 9 - 22 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 9-22, March 2019. For an infinite set X, denote by Ω(X) the semigroup of all surjective mappings from X to X. We determine Green’s relations in Ω(X), show that the kernel (unique minimum ideal) of Ω(X) exists and determine its elements and cardinality. For a countably infinite set X, we describe the elements of Ω(X) for which the ð’Ÿ-class and ð’¥-class coincide. We compare the results for Ω(X) with the corresponding results for other transformation semigroups on X. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:38Z DOI: 10.1142/S1005386719000038

Authors:Mourad Chelgham, Mohamed Kerada, Lamnouar Noui, Serkan Araci Pages: 23 - 30 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 23-30, March 2019. Let F, N, A and N2 denote the properties of being finite, nilpotent, abelian and nilpotent of classes at most 2, respectively. Firstly we consider the class of finitely generated FN-groups. We show that the property FC is closed under finite extensions, and extend this result to finitely generated NF-groups. Secondly we prove that a finitely generated NF-group G is in the class ((FC)F, ∞) if and only if G is an FA-group. Finally we prove that a finitely generated NF-group in the class ((FC)F, ∞)* is an FN2-group. Moreover, G/Z2(G) is finite. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:34Z DOI: 10.1142/S100538671900004X

Authors:Emma L. Rode Pages: 31 - 50 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 31-50, March 2019. The k-characters are class functions on subsets of Gk called the k-classes of G. For a finite group G, the k-class sums form a basis for a subring of ℂGk, which we call the k-S-ring of G, and we think of these rings as generalized centralizer rings. We show that for a finite group G the 3-S-ring determines G. More specifically, the group characters and set products of certain 3-classes of G, which we call “uniform 3-classes”, determine G. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:38Z DOI: 10.1142/S1005386719000051

Authors:Qiuhui Mo Pages: 51 - 64 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 51-64, March 2019. Bokut, Chen and Huang proved that every countably generated L-algebra over a countable field can be embedded into a simple two-generated L-algebra. In this paper, we prove that every countably generated L-algebra can be embedded into a simple two-generated L-algebra. We also prove that every anti-commutative algebra can be embedded into a simple anti-commutative algebra, and that every countably generated anti-commutative algebra can be embedded into a simple two-generated anti-commutative algebra. Finally, we prove that every anti-commutative algebra can be embedded into its universal enveloping non-associative algebra. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:43Z DOI: 10.1142/S1005386719000063

Authors:Xueyi Huang, Qiongxiang Huang Pages: 65 - 82 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 65-82, March 2019. We characterize all connected graphs with exactly three distinct normalized Laplacian eigenvalues among which one is equal to 1, and determine all connected bipartite graphs with at least one vertex of degree 1 having exactly four distinct normalized Laplacian eigenvalues. In addition, we find all unicyclic graphs with three or four distinct normalized Laplacian eigenvalues. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:36Z DOI: 10.1142/S1005386719000075

Authors:Umut Sayın, Feride Kuzucuoğlu Pages: 83 - 92 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 83-92, March 2019. Let K be a 2-torsion free ring with identity and Rn(K, J) be the ring of all n × n matrices over K such that the entries on and above the main diagonal are elements of an ideal J of K. We describe all Jordan derivations of the matrix ring Rn(K, J) in this paper. The main result states that every Jordan derivation Δ of Rn(K, J) is of the form Δ = D + Ω, where D is a derivation of Rn(K, J) and Ω is an extremal Jordan derivation of Rn(K, J). Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:41Z DOI: 10.1142/S1005386719000087

Authors:Vincenzo De Filippis, Nadeem ur Rehman Pages: 93 - 104 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 93-104, March 2019. Let R be a prime ring of characteristic different from 2, Z(R) its center, L a Lie ideal of R, and m, n, s, t ≥ 1 fixed integers with t ≤ m + n + s. Suppose that α is a non-trivial automorphism of R and let Φ(x, y) = [x, y]t – [x, y]m [α([x, y]),[x, y]]n [x, y]s. Thus, (a) if Φ(u, v) = 0 for any u, v ∈ L, then L ⊆ Z(R); (b) if Φ(u, v) ∈ Z(R) for any u, v ∈ L, then either L ⊆ Z(R) or R satisfies s4, the standard identity of degree 4. We also extend the results to semiprime rings. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:35Z DOI: 10.1142/S1005386719000099

Authors:Yakun Zhang, Guoping Tang, Hong Chen Pages: 105 - 112 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 105-112, March 2019. Let G be a finite abelian p-group, Γ the maximal ℤ-order of ℤ[G]. We prove that the 2-primary torsion subgroups of K2(ℤ[G]) and K2(Γ) are isomorphic when p ≡ 3, 5, 7 (mod 8), and [math] is isomorphic to [math] when p ≡ 2, 3, 5, 7. As an application, we give the structure of K2(ℤ[G]) for G a cyclic p-group or an elementary abelian p-group. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:46Z DOI: 10.1142/S1005386719000105

Authors:Fatemeh Cheraghi, Amir Mafi Pages: 113 - 122 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 113-122, March 2019. Let (A, ð”ª) be a commutative quasi-local ring with non-zero identity and M be an Artinian A-module with dim M = d. If I is an ideal of A with ℓ(0 :M I) < ∞, then we show that for a minimal reduction J of I, (0 :M JI) = (0 :M I2) if and only if [math] for all n ≥ 0. Moreover, we study the dual of Burch’s inequality. In particular, the Burch’s inequality becomes an equality if G(I, M) is co-Cohen-Macaulay. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:37Z DOI: 10.1142/S1005386719000117

Authors:Gang Han, Yucheng Liu, Kang Lu Pages: 123 - 138 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 123-138, March 2019. A G-grading on an algebra, where G is an abelian group, is called multiplicity-free if each homogeneous component of the grading is 1-dimensional. We introduce skew root systems of Lie type and skew root systems of Jordan type, and use them to construct multiplicity-free gradings on semisimple Lie algebras and on semisimple Jordan algebras respectively. Under certain conditions the corresponding Lie (resp., Jordan) algebras are simple. Two families of skew root systems of Lie type (resp., of Jordan type) are constructed and the corresponding Lie (resp., Jordan) algebras are identified. This is a new approach to study abelian group gradings on Lie and Jordan algebras. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:46Z DOI: 10.1142/S1005386719000129

Authors:Jia Zhang, Tingting Qiu, Long Miao, Juping Tang Pages: 139 - 146 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 139-146, March 2019. A subgroup H of G is called ℳ-supplemented in G if there exists a subgroup B of G such that G = HB and Hi B < G for every maximal subgroup Hi of H. In this paper, we use ℳ-supplemented subgroups to study the structure of finite groups and obtain some new characterization about solvability and p-supersolvability for a fixed prime p. Some results in the literature are corollaries of our theorems. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:36Z DOI: 10.1142/S1005386719000130

Authors:István Kovács, Grigory Ryabov Pages: 147 - 160 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 147-160, March 2019. A Schur ring over a finite group is said to be decomposable if it is the generalized wreath product of Schur rings over smaller groups. In this paper we establish a sufficient condition for a decomposable Schur ring over the direct product of elementary abelian groups to be a CI-Schur ring. By using this condition we offer short proofs for some known results on the CI-property for decomposable Schur rings over an elementary abelian group of rank at most 5. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:43Z DOI: 10.1142/S1005386719000142

Authors:Christos A. Pallikaros Pages: 161 - 180 Abstract: Algebra Colloquium, Volume 26, Issue 01, Page 161-180, March 2019. We obtain alternative explicit Specht filtrations for the induced and the restricted Specht modules in the Hecke algebra of the symmetric group (defined over the ring A = ℤ[q1/2, q−1/2], where q is an indeterminate) using C-bases for these modules. Moreover, we provide a link between a certain C-basis for the induced Specht module and the notion of pairs of partitions. Citation: Algebra Colloquium PubDate: 2019-03-07T09:36:35Z DOI: 10.1142/S1005386719000154