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In this paper, we generalize the main results of Guo and Isaacs, Archiv der Mathematik 105 (2015) 215-222. We also obtain some criteria for -nilpotency of a finite group. [ABSTRACT FROM AUTHOR]

In this paper we mainly study sporadic groups in terms of p-local rank, especially, the 2-local ranks of some sporadic groups are given. [ABSTRACT FROM AUTHOR]

In this paper, we study the structure of finite groups G under the assumption that certain abelian subgroups of largest possible exponent of prime power order lie in the 픉-hypercenter of G. We improve and extend some results of Ezzat, Shaalan, Elashiry, Asaad, Ramadan, and Buckley. [ABSTRACT FROM AUTHOR]

Table Algebras (A, B) with distinct non-trivial basis elements a, b ∈ B satisfying either $ab = m \overline{a} + n \overline{b}$ or $ab = m \overline{a} + nb$ for some m, n ∈ ℝ+ are studied in this paper. The case $ab = m \overline{a} + nb$ was partially classified by Arad and Blau, and the case $ab = m \overline{a} + n \overline{b}$ was partially classified by Arad and Cohen. [ABSTRACT FROM AUTHOR]

In this paper we produce a finite algebra which generates a variety with a PSPACE-complete membership problem. We produce another finite algebra with a γ function that grows exponentially. The results are obtained via a modification of a construction of the algebra A(T) that was introduced by McKenzie in 1996. [ABSTRACT FROM AUTHOR]

In this paper, we define the notion of dimension filtration of an Artinian module and study a class of Artinian modules, called sequentially co-Cohen–Macaulay modules, which contains strictly all co-Cohen–Macaulay modules. Some characterizations of co-Cohen–Macaulayness in terms of the Matlis duality and of local homology are also given. [ABSTRACT FROM AUTHOR]

For a given maximal subgroup M of a finite group G, a subgroup C of G is said to be a completion for M in G if C is not contained in M while every G-invariant proper subgroup of C is contained in M. A completion C of M is called maximal if M has no any completion which properly contains C. In this paper, the authors weaken the condition of maximal completions by defining s-completions. Using s-completions, the authors obtain some new characterizations of the solvable and supersolvable groups. [ABSTRACT FROM AUTHOR]

It is known that certain restrictions on the the character degrees or the sizes of the conjugacy classes of a group imply some structural properties of that group. In this paper, we study the effect on the structure of a group of similar restrictions on the zero sets of its irreducible characters. [ABSTRACT FROM AUTHOR]