Many Frobenius complements have even order
نویسندگان
چکیده
The theory of Frobenius groups with complements even order largely reduces to tractable algebraic number theory. If we consider only an upper bound s on the distinct primes dividing their commutator subgroups, then proportion these odd is less than 1/2s. A positive lower also given.
منابع مشابه
Groups of Prime Power Order as Frobenius-wielandt Complements
It is known that the Sylow subgroups of a Frobenius complement are cyclic or generalized quaternion. In this paper it is shown that there are no restrictions at all on the structure of the Sylow subgroups of the FrobeniusWielandt complements that appear in the well-known Wielandt's generalization of Frobenius' Theorem. Some examples of explicit constructions are also given. 0. Introduction Let ...
متن کاملFinite groups have even more centralizers
For a finite group $G$, let $Cent(G)$ denote the set of centralizers of single elements of $G$. In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent, then $Gcong S_3, D_{10}$ or $S_3times S_3$. This result gives a partial and positive answer to a conjecture raised by A. R. Ashrafi [On finite groups with a given number of centralizers, Algebra Collo...
متن کاملThe Polynomial Functions on Frobenius Complements
We determine the number of unary polynomial functions on all Frobenius complements and on all finite solvable groups all of whose abelian subgroups are cyclic. 1. Notation and results Let (G, ·) be a group. A unary polynomial function p : G → G is a function that can be written in the form p(x) := a0x a1x e1 · · · an−1xan, where n ∈ N0, a0, . . . , an are in G, and e0, . . . , en−1 are integers...
متن کاملfinite groups have even more centralizers
for a finite group $g$, let $cent(g)$ denote the set of centralizers of single elements of $g$. in this note we prove that if $|g|leq frac{3}{2}|cent(g)|$ and $g$ is 2-nilpotent, then $gcong s_3, d_{10}$ or $s_3times s_3$. this result gives a partial and positive answer to a conjecture raised by a. r. ashrafi [on finite groups with a given number of centralizers, algebra collo...
متن کاملUncountably Many Arcs in S Whose Complements Have Non-isomorphic, Indecomposable Fundamental Groups
An uncountable collection of arcs in S is constructed, each member of which is wild precisely at its endpoints, such that the fundamental groups of their complements are non-trivial, pairwise non-isomorphic, and indecomposable with respect to free products. The fundamental group of the complement of a certain Fox-Artin arc is also shown to be indecomposable.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2021
ISSN: ['1532-4125', '0092-7872']
DOI: https://doi.org/10.1080/00927872.2021.1979025