Finite permutation groups with large abelian quotients
نویسندگان
چکیده
منابع مشابه
Finite Permutation Groups with Large Abelian Quotients L . G . Kovacs and Cheryl
We show that if G is a group of permutations on a set of n points and if \ G/ G'\ denotes the order of its largest abelian quotient, then either \ G/ G'\ = 1 or there is a prime p dividing \ G/ G'\ such that \ G/ G'\ < p . Equality holds if and only if G is a p group which is the direct product of its transitive constituents, with each of those having order /?, except when p = 2 in which case o...
متن کاملRepresenting Quotients of Permutation Groups
IN this note, we consider the following problem. Let G be a finite permutation group of degree d, and let N b e a normal subgroup of G. Under what circumstances does G/N have a faithful permutation representation of degree at most di Positive answers to this question are likely to have applications to computational group theory, since there are currently no really satisfactory practical methods...
متن کاملOn a Permutation Problem for Finite Abelian Groups
LetG be a finite additive abelian group with exponent n > 1, and let a1, . . . , an−1 be elements of G. We show that there is a permutation σ ∈ Sn−1 such that all the elements saσ(s) (s = 1, . . . , n− 1) are nonzero if and only if ∣∣∣{1 6 s < n : n d as 6= 0 }∣∣∣ > d− 1 for every positive divisor d of n. When G is the cyclic group Z/nZ, this confirms a conjecture of Z.-W. Sun.
متن کاملLarge Abelian Subgroups of Finite p-Groups
It would be interesting to extend this result by allowing B to have nilpotence class 2 instead of necessarily being abelian. This cannot be done if p = 2 (Example 4.2), but perhaps it is possible for p odd. (It was done by the author ([Gor, p.274]; [HB, III, p.21]) for the special case in which p is odd and [B,B] ≤ A.) However, there is an application of Thompson’s Replacement Theorem that can ...
متن کاملGroups whose proper quotients are virtually abelian
The just non-(virtually abelian) groups with non-trivial Fitting subgroup are classified. Particular attention is given to those which are virtually nilpotent and examples are given of the interesting phenomena that can occur.
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: Pacific Journal of Mathematics
سال: 1989
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1989.136.283