EUDML

For a complex character $χ$ of a finite group $G$ , it is known that the product $sh (χ) = \prod_{l \in L (χ)} (χ (1) - l)$ is a multiple of $| G |$ , where $L (χ)$ is the image of $χ$ on $G - {1}$ . The character $χ$ is said to be a sharp character of type $L$ if $L = L (χ)$ and $sh (χ) = | G |$ . If the principal character of $G$ is not an irreducible constituent of $χ$ , then the character $χ$ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups $G$ with normalized sharp characters of type ${- 1, 0, 2}$ . Here we prove that such a group with nontrivial center is...

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Characterization of $SL (2, q)$ by its non-commuting graph.

A combinatorial problem in infinite groups.

Powers of a product of commutators as products of squares.

Some conditions on infinite subsets of infinite groups.

Finitely generated soluble groups with an Engel condition on infinite subsets

A condition on a certain variety of groups

On sharp characters of type ${- 1, 0, 2}$