On locally finite groups whose derived subgroup is locally nilpotent
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DOI: 10.1002/mana.202400263
Abstract: A celebrated theorem of Helmut Wielandt shows that the nilpotent residual of the subgroup generated by two subnormal subgroups of a finite group is the subgroup generated by the nilpotent residuals of the subgroups. This… read more here.
Keywords: locally nilpotent; finite groups; derived subgroup; subgroup generated ... See more keywords
Laws of the Lattices of $$\sigma $$-Local Formations of Finite Groups
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DOI: 10.1007/s00009-020-01510-w
Abstract: Let n be a positive integer, and let $$\sigma = \{\sigma _i \mid i \in I\}$$ be a partition of the set of all primes. It is shown that every law of the lattice of… read more here.
Keywords: local formations; finite groups; formations finite; sigma local ... See more keywords
Characterising bimodal collections of sets in finite groups
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DOI: 10.1007/s00013-019-01361-2
Abstract: A collection of disjoint subsets ${\cal A}=\{A_1,A_2,\dotsc,A_m\}$ of a finite abelian group is said to have the \emph{bimodal} property if, for any non-zero group element $\delta$, either $\delta$ never occurs as a difference between an… read more here.
Keywords: collections sets; sets finite; finite groups; element ... See more keywords
Finite groups whose subgroup graph contains a vertex of large degree
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DOI: 10.1007/s00013-025-02121-1
Abstract: Burness and Scott (J Aust Math Soc 87:329-357, 2009) classified finite groups G such that the number of prime order subgroups of G is greater than |G|/2-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}… read more here.
Keywords: subgroup graph; finite groups; graph contains; groups whose ... See more keywords
Minimal Non-Iwasawa Finite Groups
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DOI: 10.1007/s00025-018-0907-5
Abstract: In this note, we describe first the structure of minimal non-Iwasawa finite groups. Then we determine the minimal non-Iwasawa finite groups which are modular. Also, we find connections between minimal non-Iwasawa finite groups and the… read more here.
Keywords: finite groups; minimal non; iwasawa finite; non iwasawa ... See more keywords
Euler Characteristics of p-Coset Posets of Finite Groups
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DOI: 10.1007/s00373-025-02898-6
Abstract: The p-coset poset of a finite group G consists of all cosets of proper p-subgroups of G ordered by set inclusion. We determine the Euler characteristic of the p-coset poset of the finite groups of… read more here.
Keywords: posets finite; finite groups; coset posets; euler characteristics ... See more keywords
On S-semipermutable or S-permutably embedded subgroups of finite groups
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DOI: 10.1007/s10474-016-0674-2
Abstract: We extend some known results concerning S-semipermutable subgroups and S-permutably embedded subgroups. In particular, we generalize the main results of Kong [15] and Li et al. [11]. read more here.
Keywords: finite groups; semipermutable permutably; embedded subgroups; permutably embedded ... See more keywords
Finite groups with certain kind of subgroups weakly c-supplemented
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DOI: 10.1007/s10474-017-0738-y
Abstract: Let G be a finite group. A subgroup H of G is called an $${\mathcal{H}}$$H-subgroup in G if $${N_{G}(H)\cap H^{g} \leq H}$$NG(H)∩Hg≤H for all $${g\in G}$$g∈G. A subgroup H of G is called weakly c-supplemented… read more here.
Keywords: finite groups; subgroup; certain kind; weakly supplemented ... See more keywords
The influence of $$IC\Phi$$-subgroups on the structure of finite groups
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DOI: 10.1007/s10474-020-01122-6
Abstract: A subgroup $$H$$ of a group G is called an $$IC\Phi$$ -subgroup of G if $$H\cap [H,G]\leq \Phi(H)$$ . We investigate the structure of a finite group G under the assumption that some subgroups of… read more here.
Keywords: finite groups; influence phi; structure finite; phi subgroups ... See more keywords
Coleman automorphisms of finite groups with semidihedral Sylow 2-subgroups
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DOI: 10.1007/s10474-024-01408-z
Abstract: We study some families of finite groups having inner class-preserving automorphisms. In particular, let G be a finite group and S be a semidihedral Sylow 2-subgroup. Then, in both cases when either Sym(4) is not… read more here.
Keywords: automorphisms finite; semidihedral sylow; finite groups; coleman automorphisms ... See more keywords
On the Relationships Between Central Series in Some Locally Finite Groups
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DOI: 10.1007/s11253-017-1318-6
Abstract: It is shown that the class of locally finite divisible-by-bounded groups is both a Schur class and a Baer class. read more here.
Keywords: relationships central; finite groups; series locally; class ... See more keywords