For simplicity, we use the following convention: G is a group, a, b are elements of G, m, n are natural numbers, and p is a prime natural number. One can prove the following propositions: (1) If for every natural number r holds n 6= pr, then there exists an element s of N such that s is prime and s | n and s 6= p. (2) For all natural numbers n, m such that n | pm there exists a natural number r...

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

We observe that, for fixed n ≥ 3, each of the Artin groups of finite type An, Bn = Cn, and affine type Ãn−1 and C̃n−1 is a central extension of a finite index subgroup of the mapping class group of the (n + 2)-punctured sphere. (The centre is trivial in the affine case and infinite cyclic in the finite type cases). Using results of Ivanov and Korkmaz on abstract commensurators of surface mapping...

We study irreducible unitary representations of the three rst jet (or Leibniz) extensions G k m of a compact group G, focusing on the neighborhood of the trivial representation. We also describe some associated irreducible unitary (continuous tensor product) representations of the gauge (or current) groups of mappings from a Riemannian manifold into G k m .

We investigate the first two Galois cohomology groups of p-extensions over a base field which does not necessarily contain a primitive pth root of unity. We use twisted coefficients in a systematic way. We describe field extensions which are classified by certain residue classes modulo pnth powers of a related field, and we obtain transparent proofs and slight generalizations of some classical ...