Archiv der Mathematik最新文献

In this paper, we consider Pogorelov type estimates up to the flat boundary for k-convex solutions of sum Hessian equations with right hand term f(x, u).

In this article, we prove results about finite soluble groups that act with fixity 2 or 3.

The question of whether the group ({mathbb {Q}}_p rtimes {mathbb {Q}}_p^*) is Hermitian has been stated as an open question in multiple sources in the literature, even as recently as a paper by R. Palma published in 2015. In this note, we confirm that this group is Hermitian by proving the following more general theorem: given any local field ({mathbb {K}}), the affine group ({mathbb {K}} rtimes {mathbb {K}}^*) is a Hermitian group. The proof is a consequence of results about Hermitian Banach (*)-algebras from the 1970s. In the case that ({mathbb {K}}) is a non-archimedean local field, this result produces examples of totally disconnected locally compact Hermitian groups with exponential growth, and these are the first examples of groups satisfying these properties. This answers a second question of Palma about the existence of such groups.

In this note, we provide some nilpotency criteria for the terms of the lower central series of a finite group involving the order of their standard generators. Moreover, when the finite group is solvable, we provide a characterization for the nilpotency of the terms of the derived series of the group.

In this article, we present a combinatorial formula for the Wedderburn decomposition of rational group algebras of Camina p-groups, where p is a prime. We also provide a complete set of primitive central idempotents of rational group algebras of these groups.

A relevant property of spanned vector bundles of rank N on a normal projective variety of dimension N having top Chern class 1 is presented and several examples are discussed. Moreover, such vector bundles with ample determinant are classified for (N=2).

Let K be a field equipped with a Henselian valuation, and let D be a tame central division algebra over the field K. Denote by (textrm{TK}_1(D)) the torsion subgroup of the Whitehead group (textrm{K}_1(D) = D^*/D'), where (D^*) is the multiplicative group of D and (D') is its derived subgroup. Let (textbf{G}) be the subgroup of (D^*) such that (textrm{TK}_1(D) = textbf{G}/D'). In this note, we prove that either ((1 + M_D) cap textbf{G} subseteq D'), or the residue field (overline{K}) has characteristic (p > 0) and the group (textbf{H}:= ((1 + M_D) cap textbf{G})D'/D') is a p-group. Additionally, we provide examples of valued division algebras with non-trivial (textbf{H}). This illustrates that, in contrast to the reduced Whitehead group (textrm{SK}_1(D)), a complete analogue of the congruence theorem does not hold for (textrm{TK}_1(D)).

For a finite group G,  the intersection number (alpha (G)) of G is the minimal number of maximal subgroups of G whose intersection coincides with (Phi (G),) the Frattini subgroup of G. In this paper, new upper bounds on (alpha (G)) are established when G is soluble.

Let (mathscr {L}(mathscr {H})) be the algebra of all bounded linear operators on a complex Hilbert space (mathscr {H}). For an operator (Tin mathscr {L}(mathscr {H})), let (W_0(T)) be the maximal numerical range of T. We show that a map (varphi ) from (mathscr {L}(mathscr {H})) onto itself satisfies

if and only if there are a unitary operator (Uin mathscr {L}(mathscr {H})) and (lambda in mathbb {C}) such that (lambda ^3=1) and either (varphi (T)= lambda UTU^*) for all (Tin mathscr {L}(mathscr {H})), or (varphi (T)= lambda UT^top U^*) for all (Tin mathscr {L}(mathscr {H})). Here, (T^top ) denotes the transpose of any operator (Tin mathscr {L}(mathscr {H})) relative to a fixed but arbitrary orthonormal base of (mathscr {H}). When the triple product “STS” is replaced by the skew-triple product “(TS^*T)”, we arrive at the same conclusion but with (lambda =1).

Let R be an associative ring with identity. We establish that the generalized Auslander–Reiten conjecture implies the Wakamatsu tilting conjecture. Furthermore, we prove that any Wakamatsu tilting R-module of finite projective dimension that is tensorly faithful is projective. By utilizing this result, we show the validity of the Wakamatsu tilting conjecture for R in two cases: when R is a left Artinian local ring or when it is the group ring of a finite group G over a commutative Artinian ring.