Zobrazeno 1 - 10
of 232
pro vyhledávání: '"20e15"'
Starting with an integral domain $D$ of characteristic $0$, we consider a class of iterated wreath product $W_n$ of $n$ copies of $D$. In order that $W_n$ be transfinite hypercentral, it is necessary to restrict to the case of wreath products defined
Externí odkaz:
http://arxiv.org/abs/2411.03846
J. S. Wilson proved in 1971 an isomorphism between the structural lattice associated to a group belonging to his second class of groups with every proper quotient finite and the Boolean algebra of clopen subsets of Cantor's ternary set. In this paper
Externí odkaz:
http://arxiv.org/abs/2409.01655
In this paper, we revisit the 1979 work of Isbell on subfactors of groups and their projections, which he uses to establish a stronger formulation of the butterfly lemma and its consequence, the refinement theorem for subnormal series of subgroups. W
Externí odkaz:
http://arxiv.org/abs/2408.05731
Autor:
Corson, Samuel M., Shelah, Saharon
A group is Artinian if there is no infinite strictly descending chain of subgroups. Ol'shanskii has asked whether there are Artinian groups of arbitrarily large cardinality. We show that this problem is essentially the same as an analogous question,
Externí odkaz:
http://arxiv.org/abs/2408.03201
Autor:
Labute, John
In this article we trace the genesis of a theorem that gives for the first time examples of Galois group $G_S$ of the maximal $p$-extension of $\mathbb{Q}$, unramified outside a finite set of primes not containing $p$, that are of cohomological dimen
Externí odkaz:
http://arxiv.org/abs/2406.08233
Autor:
Cocke, William, McCulloch, Ryan
The Chermak-Delgado measure of a finite group is a function which assigns to each subgroup a positive integer. In this paper, we give necessary and sufficient conditions for when the Chermak-Delgado measure of a group is actually a map of posets, i.e
Externí odkaz:
http://arxiv.org/abs/2401.12450
Autor:
Zangurashvili, Dali
It is shown that a nontrivial normal subgroup $N$ of a group $G$ is a free factor of the $N$'s normal closure in the $G$'s free product with arbitrary nontrivial groups.
Externí odkaz:
http://arxiv.org/abs/2401.03335
Autor:
Ferrara, Maria, Trombetti, Marco
Let $\sigma=\{\sigma_j\,:\, j\in J\}$ be a partition of the set $\mathbb{P}$ of all prime numbers. A subgroup $X$ of a finite group $G$ is~\textit{$\sigma$-subnormal} in $G$ if there exists a chain of subgroups $$X=X_0\leq X_1\leq\ldots\leq X_n=G$$ s
Externí odkaz:
http://arxiv.org/abs/2310.03391
Autor:
Roney-Dougal, Colva M., Wu, Peiran
An irredundant base of a group $G$ acting faithfully on a finite set $\Gamma$ is a sequence of points in $\Gamma$ that produces a strictly descending chain of pointwise stabiliser subgroups in $G$, terminating at the trivial subgroup. Suppose that $G
Externí odkaz:
http://arxiv.org/abs/2309.00092
Let $G$ be a locally graded group and suppose that every non-nilpotent subgroup of $G$ is permutable. We prove that $G$ is soluble. (In light of previous results of the authors, it suffices to prove that $G$ is soluble if it is periodic.
Externí odkaz:
http://arxiv.org/abs/2308.04433