Finite groups and $k$-submodular subgroups

T. I. Vasilyeva

Finite groups and $k$-submodular subgroups

Group Theory 2025-05-21 v2

Authors: T. I. Vasilyeva

Abstract

For natural numbers $n$ and $k$ , the concepts of $n$ -modularly embedded subgroup, $k$ -submodular subgroup and $k$ - $\mathrm{LM}$ -group are given, which generalize, respectively, the concepts of modular subgroup, submodular subgroup and $\mathrm{LM}$ -group. Classes of groups with given systems of $k$ -submodular subgroups are investigated.

Keywords

finite group theory semigroup theory module theory

Cite

@article{arxiv.2406.04704,
  title  = {Finite groups and $k$-submodular subgroups},
  author = {T. I. Vasilyeva},
  journal= {arXiv preprint arXiv:2406.04704},
  year   = {2025}
}

Comments

16 pages. This article is an expanded and revised version. Definitions 1 and 2 have been clarified to remove unnecessary conditions. The main results are supplemented either by new equivalent conditions or by new items. Examples and comments are given. A new concept of k-LM-group has been introduced. Some new results have been proven. New sources have been added to References

Finite groups and $k$-submodular subgroups

Abstract

Keywords

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