For a finite group [Formula: see text], let text] denote the sum of element orders text]. If is positive integer be cyclic order It known that maximum value on set groups and if only In this paper, we investigate second largest structure with when odd.

Let x be an element of prime order, p, in a finite group, G, and let P be a p-Sylow subgroup of G containing x. Say that x satisfies the unique conjugacy condition (u.c.c.) relative to G and the p-Sylow subgroup P if x is not conjugate in G to any other element of P. Let 02'(G) denote the largest normal subgroup of G oi odd order. Define the subgroup Z*(G) by the equation Z*(G)/0v(G)=Z(G/0v(G))...

A theorem now known as Sperner's Lemma [5] states that a largest collection of subsets of an n-element set such that no subset contains another is obtained by taking the collection of all the subsets with cardinal [n/2\. (We denote by |*J, resp. [*], the largest integer less than or equal to x, resp. the smallest integer greater than or equal to x.) In other words, the density of a largest anti...

let $g $ be a finite group and let $gamma(g)$ be the prime graph‎ ‎of g‎. ‎assume $2 < q = p^{alpha} < 100$‎. ‎we determine finite groups‎ ‎g such that $gamma(g) = gamma(u_3(q))$ and prove that if $q neq‎ ‎3‎, ‎5‎, ‎9‎, ‎17$‎, ‎then $u_3(q)$ is quasirecognizable by prime graph‎, ‎i.e‎. ‎if $g$ is a finite group with the same prime graph as the‎ ‎finite simple group $u_3(q)$‎, ‎then $g$ has a un...

We prove local inverse-type estimates for the four non-local boundary integral operators associated with the Laplace operator on a bounded Lipschitz domain Ω in R for d ≥ 2 with piecewise smooth boundary. For piecewise polynomial ansatz spaces and d ∈ {2, 3}, the inverse estimates are explicit in both the local mesh width and the approximation order. An application to efficiency estimates in a ...

In boundary element analysis, first order function derivatives, e.g., boundary potential gradient or stress tensor, can be accurately computed by evaluating the hypersingular integral equation for these quantities. However, this approach requires a complete integration over the boundary and is therefore computationally quite expensive. Herein it is shown that this method can be significantly si...