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Simple proofs of some generalizations of the Wilson’s theorem

Jan Górowski, Adam Łomnicki (2014)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

In this paper a remarkable simple proof of the Gauss’s generalization of the Wilson’s theorem is given. The proof is based on properties of a subgroup generated by element of order 2 of a finite abelian group. Some conditions equivalent to the cyclicity of (Φ(n), ·n), where n > 2 is an integer are presented, in particular, a condition for the existence of the unique element of order 2 in such a group.

Simulated factorizations II.

A.D. Sands (1992)

Aequationes mathematicae

Solitary quotients of finite groups

Marius Tărnăuceanu (2012)

Open Mathematics

We introduce and study the lattice of normal subgroups of a group G that determine solitary quotients. It is closely connected to the well-known lattice of solitary subgroups of G, see [Kaplan G., Levy D., Solitary subgroups, Comm. Algebra, 2009, 37(6), 1873–1883]. A precise description of this lattice is given for some particular classes of finite groups.

Displaying 1 – 10 of 10

Simple proofs of some generalizations of the Wilson’s theorem

Simulated factorizations II.

Solitary quotients of finite groups

Some problems on splittings of groups.

Some values of Olson's constant.

Sophie Germain little suns

Splitting groups of prime order.

Splittings of Abelian groups by integers.

Splittings of Abelian groups by integers. (Short Communication).

Subsums of a zero-sum free subset of an abelian group.

Currently displaying 1 – 10 of 10