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The first examples of formations which are arboreous (and therefore Hall) but not freely indexed (and therefore not locally extensible) are found. Likewise, the first examples of solvable formations which are freely indexed and arboreous (and therefore Hall) but not locally extensible are constructed. Some open questions are also mentioned.
Throughout this paper, all groups are finite. Let $sigma ={sigma_{i} | iin I }$ be some partition of the set of all primes $Bbb{P}$. If $n$ is an integer, the symbol $sigma (n)$ denotes the set ${sigma_{i} |sigma_{i}cap pi (n) e emptyset }$. Th
In this paper, we study a group in which every 2-maximal subgroup is a Hall subgroup.
We construct several series of explicit presentations of infinite hyperbolic groups enjoying Kazhdans property (T). Some of them are significantly shorter than the previously known shortest examples. Moreover, we show that some of those hyperbolic Ka
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.
The power graph $mathcal{P}(G)$ of a finite group $G$ is the graph whose vertex set is $G$, and two elements in $G$ are adjacent if one of them is a power of the other. The purpose of this paper is twofold. First, we find the complexity of a clique--