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Cayley's Theorem

Artur Korniłowicz (2011)

Formalized Mathematics

The article formalizes the Cayley's theorem saying that every group G is isomorphic to a subgroup of the symmetric group on G.

Collineation group as a subgroup of the symmetric group

Fedor Bogomolov, Marat Rovinsky (2013)

Open Mathematics

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 𝔖 ψ 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.,...

Crossed product of cyclic groups

Ana-Loredana Agore, Dragoş Frățilă (2010)

Czechoslovak Mathematical Journal

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.

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