On the Crossing of Maximal Subgroups of Finite Groups
Sign Up to like & getrecommendations! Published in 2020 at "Ukrainian Mathematical Journal"
DOI: 10.1007/s11253-020-01740-x
Abstract: We establish the structure of normal subgroups in θ -Frattini extensions, where θ is a subgroup functor. For a local Fitting structure F $$ \mathfrak{F} $$ containing all nilpotent groups, it is shown that, in… read more here.
Keywords: finite groups; maximal subgroups; structure; mathfrak ... See more keywords
Maximal Subgroups of Almost Subnormal Subgroups in Division Rings
Sign Up to like & getrecommendations! Published in 2021 at "Acta Mathematica Vietnamica"
DOI: 10.1007/s40306-021-00456-9
Abstract: In this paper, we investigate maximal subgroups of an almost subnormal subgroup G in a division ring D whose center is infinite. Among results, we prove that if M is such a maximal subgroup, then… read more here.
Keywords: almost subnormal; subgroups almost; subnormal subgroups; subgroups division ... See more keywords
Maximal subgroups of groups of intermediate growth
Sign Up to like & getrecommendations! Published in 2018 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2018.10.026
Abstract: Abstract Finding the number of maximal subgroups of infinite index of a finitely generated group is a natural problem that has been solved for several classes of “geometric” groups (linear groups, hyperbolic groups, mapping class… read more here.
Keywords: maximal subgroups; groups intermediate; subgroups infinite; infinite index ... See more keywords
GENERATION OF SECOND MAXIMAL SUBGROUPS AND THE EXISTENCE OF SPECIAL PRIMES
Sign Up to like & getrecommendations! Published in 2017 at "Forum of Mathematics, Sigma"
DOI: 10.1017/fms.2017.21
Abstract: Let $G$ be a finite almost simple group. It is well known that $G$ can be generated by three elements, and in previous work we showed that 6 generators suffice for all maximal subgroups of… read more here.
Keywords: maximal subgroups; generation second; second maximal; subgroups existence ... See more keywords
OVERGROUPS OF WEAK SECOND MAXIMAL SUBGROUPS
Sign Up to like & getrecommendations! Published in 2018 at "Bulletin of the Australian Mathematical Society"
DOI: 10.1017/s0004972718000904
Abstract: A subgroup $H$ is called a weak second maximal subgroup of $G$ if $H$ is a maximal subgroup of a maximal subgroup of $G$ . Let $m(G,H)$ denote the number of maximal subgroups of $G$… read more here.
Keywords: subgroup; overgroups weak; maximal subgroups; maximal subgroup ... See more keywords
Intersections of maximal subgroups in prosolvable groups
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Algebra"
DOI: 10.1080/00927872.2019.1566918
Abstract: Abstract Given a positive real number we say that an open subgroup H of a profinite group G is an η-intersection if there exists a family of maximal subgroups such that and . We study… read more here.
Keywords: intersection; intersections maximal; subgroups prosolvable; maximal subgroups ... See more keywords
On critical conditions of overgroups of weak second maximal subgroups
Sign Up to like & getrecommendations! Published in 2021 at "Communications in Algebra"
DOI: 10.1080/00927872.2021.1888964
Abstract: Abstract A subgroup H of a finite group G is called a weak second maximal subgroup of G if there exists a maximal subgroup M of G such that H is a maximal subgroup of… read more here.
Keywords: maximal subgroups; maximal subgroup; second maximal; critical conditions ... See more keywords
GGS-groups acting on trees of growing degrees
Sign Up to like & getrecommendations! Published in 2024 at "Communications in Algebra"
DOI: 10.1080/00927872.2025.2525388
Abstract: Abstract We consider analogues of Grigorchuk-Gupta-Sidki (GGS-)groups acting on trees of growing degree; the so-called growing GGS-groups. These groups are not just infinite and do not possess the congruence subgroup property, but many of them… read more here.
Keywords: growing degrees; groups acting; trees growing; maximal subgroups ... See more keywords
Finite Groups Whose n-Maximal Subgroups Are Modular
Sign Up to like & getrecommendations! Published in 2018 at "Siberian Mathematical Journal"
DOI: 10.1134/s0037446618030187
Abstract: Let G be a finite group. If Mn< Mn−1< · · · < M1< M0 = G with Mi a maximal subgroup of Mi−1 for all i = 1,..., n, then Mn (n > 0)… read more here.
Keywords: finite groups; subgroup; maximal subgroups; whose maximal ... See more keywords
On Prime Spectrum of Maximal Subgroups in Finite Groups
Sign Up to like & getrecommendations! Published in 2018 at "Algebra Colloquium"
DOI: 10.1142/s1005386718000408
Abstract: For a positive integer n, we denote by π(n) the set of all prime divisors of n. For a finite group G, the set [Formula: see text] is called the prime spectrum of G. Let… read more here.
Keywords: maximal subgroups; see text; formula see; prime spectrum ... See more keywords
On the ????-hypercenter and the intersection of ????-maximal subgroups of a finite group
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Group Theory"
DOI: 10.1515/jgth-2017-0043
Abstract: Abstract Let ????{\mathfrak{X}} be a class of groups. A subgroup U of a group G is called ????{\mathfrak{X}}-maximal in G provided that (a) U∈????{U\in\mathfrak{X}}, and (b) if U≤V≤G{U\leq V\leq G} and V∈????{V\in\mathfrak{X}}, then U=V{U=V}. A… read more here.
Keywords: hypercenter intersection; maximal subgroups; group; mathfrak ... See more keywords