Related papers: Finite simple groups with some abelian Sylow subgr…
In this short article, we give a summary of the Sylow $p$-subgroups of the finite simple groups of classical Lie type.
We classify closed abelian subgroups of the simple groups $G_2$, $F_4$, $Aut(so(8))$ having centralizer the same dimension as the dimension of the subgroup, as well as finite abelian subgroups of certain spin and half-spin groups having…
We consider abelain subgroups of small index in finite groups. More generally, we consider subgroups such that the product of their index by the index of their centralizer is small.
In this note, we study the finite groups with the number of cylic subgroups no greater than 6.
The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.
We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup.
We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.
We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.
The spectrum of a finite group is the set of orders of its elements. We are concerned with finite groups having the same spectrum as a direct product of nonabelian simple groups with abelian Sylow $2$-subgroups. For every positive integer…
In our previous paper, we gave a complete list of the finite non-abelian simple groups whose holomorph contains a solvable regular subgroup. In this paper, we refine our previous work by considering all finite almost simple groups. In…
In this paper, we determine the finite groups with a Sylow $r$-subgroup contained in a unique maximal subgroup. The proof involves a reduction to almost simple groups, and our main theorem extends earlier work of Aschbacher in the special…
In this article we present an extensive survey on the developments in the theory of non-abelian finite groups with abelian automorphism groups, and pose some problems and further research directions.
This is the third and final installment of an exposition of an ACL2 formalization of finite group theory. Part I covers groups and subgroups, cosets, normal subgroups, and quotient groups. Part II extends the theory in the developmnent of…
This paper deals with the number of subgroups of a given exponent in a finite abelian group. Explicit formulas are obtained in the case of rank two and rank three abelian groups. An asymptotic formula is also presented.
The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for…
In this note we describe the finite groups $G$ having $|G|-2$ cyclic subgroups. This partially solves the open problem in the end of \cite{3}.
In this short note, we describe the finite groups $G$ having $|G|-1$ cyclic subgroups. This leads to a nice characterization of the symmetric group $S_3$.
We find the nonabelian finite simple groups with order prime divisors not exceeding 1000. More generally, we determine the sets of nonabelian finite simple groups whose maximal order prime divisor is a fixed prime less than 1000. Our…
This paper provides the first steps in classifying the finite solvable groups having Property A, which is a property involving abelian normal subgroups. We see that this classification is reduced to classifying the solvable Chermak-Delgado…
We observe that abelian subgroups of Helly groups are finitely generated, and consequently, soluble subgroups of Helly groups are virtually abelian.