Cayley's Theorem
The article formalizes the Cayley's theorem saying that every group G is isomorphic to a subgroup of the symmetric group on G.
Classification of Sn-normal semigroups.
Collineation group as a subgroup of the symmetric group
Let ψ be the projectivization (i.e., the set of one-dimensional vector subspaces) of a vector space of dimension ≥ 3 over a field. Let H be a closed (in the pointwise convergence topology) subgroup of the permutation group of the set ψ. Suppose that H contains the projective group and an arbitrary self-bijection of ψ transforming a triple of collinear points to a non-collinear triple. It is well known from [Kantor W.M., McDonough T.P., On the maximality of PSL(d+1,q), d ≥ 2, J. London Math. Soc.,...
Constructing a maximal cofinitary group.
Constructing matrix geometric means.
Coset representatives for permutation groups
Crossed product of cyclic groups
All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.