arXiv subjects

Mihai-Silviu Lazorec

Publications and source records attributed to Mihai-Silviu Lazorec.

24 records · Page 2Linked to original sources

arXiv2018

Relative cyclic subgroup commutativity degrees of finite groups

In this paper we introduce and study the relative cyclic subgroup commutativity degrees of a finite group. We show that there is a finite group with $n$ such degrees for all $n \in \mathbb{N}^*\setminus \lbrace 2\rbrace$ and we indicate some classes of finite groups with few relative cyclic subgroup commutativity degrees. Using this new concept, we are able to show that the set containing all cyclic subgroup commutativity degrees of finite groups is not dense in $[0, 1]$.

math.GR↗

arXiv2018

Finite groups with two relative subgroup commutativity degrees

In this paper we show that there is an infinite number of finite groups with two relative subgroup commutativity degrees. Also, we indicate a sufficient condition such that a finite group has at least three relative subgroup commutativity degrees and we prove that $D_6$ is the only finite dihedral group with two relative commutativity degrees. Finally, we study the density of the set containing all subgroup commutativity degrees of finite groups.

math.GR↗

arXiv2017

Probabilistic aspects of ZM-groups

In this paper we study probabilistic aspects such as (cyclic) subgroup commutativity degree and (cyclic) factorization number of ZM-groups. We show that these quantities can be computed using the sizes of the conjugacy classes of these groups. In the end, we point out a class of groups whose (cyclic) subgroup commutativity degree vanishes asymptotically.

math.GR↗

arXiv2017

Cyclic factorization numbers of finite groups

In this paper we introduce and study the concept of cyclic factorization number of a finite group G. By using the Mobius inversion formula and other methods involving the cyclic subgroup structure, this is explicitly computed for some important classes of finite groups.

math.GR↗

arXiv2016

On some probabilistic aspects of (generalized) dicyclic groups

In this paper we study probabilistic aspects such as subgroup commutativity degree and cyclic subgroup commutativity degree of the (generalized) dicyclic groups. We find explicit formulas for these concepts and we provide another example of a class of groups whose (cyclic) subgroup commutativity degree vanishes asymptotically.

math.GR↗

arXiv2016

Cyclic subgroup commutativity degrees of finite groups

In this paper we introduce and study the concept of cyclic subgroup commutativity degree of a finite group $G$. This quantity measures the probability of two random cyclic subgroups of $G$ commuting. Explicit formulas are obtained for some particular classes of groups. A criterion for a finite group to be an Iwasawa group is also presented.

math.GR↗