Related papers: A characterization of ZM-groups
In this note, we study a certain class of trigonometric series which is important in many problems. An unproved statement in Zygmund's book [5] will be proved and generalized. Further discussions based on this problem will also be made…
We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.
Kuz'min (1996) characterized groups having Wirtinger presentations in relation to their second group homology. In this paper, we further refine the relation between these groups and their second group homology.
Recently, Wang and Ma propose a conjecture associated with the possible generalization of Andrews-Warnaar identities. It is confirmed in this paper. As the applications of this conjecture, we prove that a family of series can be expressed…
We define a partition of a reductive group into finitely many subsets, refining the partition of the group into strata. We state some conjectural properties of these subsets (called substrata) and verify them in some examples.
We show that for various natural classes of groups and appropriately defined K- and L-theoretic functors, injectivity or bijectivity of the assembly map follows from the Isomorphism Conjecture being true for acyclic groups lying within that…
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.
We study models M of set theory that are "condensable", in the sense that there is an "ordinal" v of M such that the rank initial segment of M determined by v is both isomorphic to M, and also an elementary submodel of M for infinitary…
This is the second one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple unitary groups.
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.
In this note we axiomatize the classes of rudimentary functions, primitive recursive functions, safe recursive set functions, and predicatively computable functions.
We show that a group is a GVZ-group if and only if it is a flat group. We show that the nilpotence class of a GVZ-group is bounded by the number of distinct degrees of irreducible characters. We also show that certain CM-groups can be…
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
We give a new proof of Glauberman's ZJ Theorem, in a form that clarifies the choices involved and offers more choices than classical treatments. In particular, we introduce two new ZJ-type subgroups of a $p$-group $S$, that contain…
In this paper, we will prove some sufficient conditions for the solvability of groups.
Given an o-minimal structure ${\mathcal M}$ with a group operation, we show that for a properly convex subset $U$, the theory of the expanded structure ${\mathcal M}'=({\mathcal M},U)$ has definable Skolem functions precisely when…
We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.
We prove the Effective Bogomolov Conjecture, and so the Bogomolov Conjecture, over a function field of characteristic 0 by proving Zhang's Conjecture about certain invariants of metrized graphs. In the function field case, these conjectures…
The purpose of this short note, is to rewrite Morozov's formula for correlation functions over the unitary group, in a much simpler form, involving the computation of a single determinant.
In this paper, we count the number of conjugacy and automorphism-conjugacy classes of elements of a ZM-group. The size of a conjugacy class with respect to these two equivalence relations is also counted.