Finite direct sums controlled by finitely many permutations

Finite Models and Finitely Many

This paper is a survey of results on nite variable logics in nite model theory. It focusses on the common underlying techniques that unite many such results.

Finite Models and Finitely Many Variables

Cards, permutations, and sums

We are given four cards, each containing four nonnegative real numbers, written one below the other, so that the sum of the numbers on each card is 1. We are allowed to put the cards in any order we like, then we write down the first number from the first card, the second number from the second card, the third number from the third card, and the fourth number from the fourth card, and we add th...

Some rank equalities for finitely many tripotent matrices

‎A rank equality is established for the sum of finitely many tripotent matrices via elementary block matrix operations‎. ‎Moreover‎, ‎by using this equality and Theorems 8 and 10 in [Chen M‎. ‎and et al‎. ‎On the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications‎, ‎The Scientific World Journal 2014 (2014)‎, ‎Article ID 702413‎, ‎7 page...

On solubility of groups with finitely many centralizers

For any group G, let C(G) denote the set of centralizers of G.We say that a group G has n centralizers (G is a Cn-group) if |C(G)| = n.In this note, we prove that every finite Cn-group with n ≤ 21 is soluble andthis estimate is sharp. Moreover, we prove that every finite Cn-group with|G| < 30n+1519 is non-nilpotent soluble. This result gives a partial answer to aconjecture raised by A. Ashrafi in ...