Article
Mathematics
Lijian An
Summary: This paper proves that for any finite abelian group A, there exists a finite group G such that the Chermak-Delgado lattice of G is a subgroup lattice of A.
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
(2023)
Article
Mathematics
Lijian An
Summary: This paper focuses on finite groups whose Chermak-Delgado lattice is a subgroup lattice of an elementary abelian p-group, proving that such groups are nilpotent of class 2. It also demonstrates that for any elementary abelian p-group E, there exists a finite group G such that the Chermak-Delgado lattice of G is a subgroup lattice of E.
COMMUNICATIONS IN ALGEBRA
(2022)
Article
Mathematics
Marius Tarnauceanu
Summary: In this note, we discuss the relationship between the number of isolated subgroups and the subgroup lattice in a finite group G. We provide descriptions of finite groups G such that the number of isolated subgroups is |L(G)| - k, where k = 0, 1, 2.
PUBLICATIONES MATHEMATICAE DEBRECEN
(2023)
Article
Mathematics
Georgiana Fasola, Marius Tarnauceanu
Summary: In this note, we investigate the subgroup lattice and Chermak-Delgado lattice of finite group G, and determine the finite groups G that satisfy certain conditions.
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics
Jiwei Zheng, Wei Zhou, D. E. Taylor
Summary: This article discusses the subgroup G(m) generated by the elements g(m), where g runs through the group G, and the nonpower subgroups of G. Then, it classifies the groups with at most nine nonpower subgroups.
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Mattia Brescia
Summary: In this paper, we study groups with finite order conjugacy classes and normal subgroups, and explore the properties of FC-groups under the chain conditions of few subnormal non-normal subgroups.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Shitian Liu, Runshi Zhang
Summary: This paper identifies the structures of non-solvable groups whose all proper subgroups have at most seven character values.
Article
Mathematics, Applied
M. Ferrara, M. Trombetti
Summary: In this short paper, a method is described for identifying pure subgroups of an abelian group by examining how the subgroup lattice embeds, all within a local nilpotent context for a general definition of purity.
RICERCHE DI MATEMATICA
(2021)
Article
Mathematics, Applied
Victor Monakhov, Irina Sokhor
Summary: The paper investigates groups with subpermuteral and strongly subpermuteral subgroups. New characterisations of supersoluble, w-supersoluble, and v-supersoluble groups are obtained. The structure of groups with all Sylow subgroups subpermuteral and also groups with all Sylow normalizers subpermuteral is described.
RESULTS IN MATHEMATICS
(2022)
Article
Mathematics
Fausto De Mari
Summary: The research focuses on characterizing locally graded groups based on the type of their subgroups and the conditions they satisfy, with an emphasis on the characteristics and rank conditions of non-modular subgroups. It investigates (generalized) soluble groups with finitely generated non-modular subgroups.
JOURNAL OF ALGEBRA
(2021)
Article
Mathematics
Bin Hu, Jianhong Huang, Dou Song, Ina N. Safonova
Summary: The article discusses the characteristics of subgroups in finite groups, as well as the definitions and properties of K-F-subnormal and K-lattice. By proving that when F is a hereditary K-lattice saturated formation containing all nilpotent groups, for a finite group G satisfying specific conditions, the derived subgroup G' belongs to F.
COMMUNICATIONS IN ALGEBRA
(2021)
Article
Mathematics
Lijian An
Summary: This paper investigates centrall large subgroups (CL-subgroups) and their minimal forms in finite groups. It extends previous work and provides a negative answer to a conjecture.
JOURNAL OF ALGEBRA
(2022)
Article
Computer Science, Theory & Methods
F. J. Talavera, S. Ardanza-Trevijano, J. Bragard, J. Elorza
Summary: This work studies when an aggregation operator preserves the structure of T-subgroup of groups whose subgroup lattice is a chain, and discusses the importance of the dominance relation between the aggregation operator and the t-norm.
FUZZY SETS AND SYSTEMS
(2023)
Article
Mathematics
Wolfgang Herfort, Karl H. Hofmann, Francesco G. Russo
Summary: This paper provides a detailed description of all totally disconnected locally compact groups with only compact elements, in which any two closed subgroups are permutable and their product remains a closed subgroup. This work sharpens the classification results in Section 14 of reference [2] without being dependent on them.
ADVANCES IN MATHEMATICS
(2021)
Article
Mathematics
M. N. Konovalova, V. S. Monakhov, I. L. Sokhor
Summary: The statement proves that the requirement for F-subnormality of all strictly 2-maximal subgroups is equivalent to the requirement for subnormality of all 2-maximal subgroups, and also shows that G is a non-nilpotent group with all proper subgroups being abelian.
COMMUNICATIONS IN ALGEBRA
(2022)