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Notes on countable extensions of  p ω + n -projectives

Peter Vassilev Danchev (2008)

Archivum Mathematicum

We prove that if G is an Abelian p -group of length not exceeding ω and H is its p ω + n -projective subgroup for n ∈ ℕ ∪ { 0 } such that G / H is countable, then G is also p ω + n -projective. This enlarges results of ours in (Arch. Math. (Brno), 2005, 2006 and 2007) as well as a classical result due to Wallace (J. Algebra, 1971).

Notes on semimedial semigroups

Fitore Abdullahu, Abdullah Zejnullahu (2009)

Commentationes Mathematicae Universitatis Carolinae

The class of semigroups satisfying semimedial laws is studied. These semigroups are called semimedial semigroups. A connection between semimedial semigroups, trimedial semigroups and exponential semigroups is presented. It is proved that the class of strongly semimedial semigroups coincides with the class of trimedial semigroups and the class of dimedial semigroups is identical with the class of exponential semigroups.

Notes on the average number of Sylow subgroups of finite groups

Jiakuan Lu, Wei Meng, Alexander Moretó, Kaisun Wu (2021)

Czechoslovak Mathematical Journal

We show that if the average number of (nonnormal) Sylow subgroups of a finite group is less than 29 4 then G is solvable or G / F ( G ) ≅ A 5 . This generalizes an earlier result by the third author.

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