Implications of the index of a fixed point subgroup

Download

index.pdf

Date

2019-01-01

Author

Turkan, Erkan Murat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

208
views

0
downloads

Let G be a finite group and A <= Aut(G). The index vertical bar G:C-G(A)vertical bar is called the index of A in G and is denoted by Ind(G)(A). In this paper, we study the influence of Ind(G)(A) on the structure of G and prove that [G, A] is solvable in case where A is cyclic, Ind G(A) is squarefree and the orders of G and A are coprime. Moreover, for arbitrary A <= Aut(G) whose order is coprime to the order of G, we show that when [G, A] is solvable, the Fitting height of [G, A] is bounded above by the number of primes (counted with multiplicities) dividing Ind(G)(A) and this bound is best possible.

Subject Keywords

Mathematical Physics, Geometry and Topology, Algebra and Number Theory, Analysis

URI

https://hdl.handle.net/11511/63724

Journal

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA

DOI

https://doi.org/10.4171/rsmup/26

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Some sufficient conditions for p-nilpotency of a finite group Kızmaz, Muhammet Yasir (Informa UK Limited, 2019-09-02) Let G be a finite group and let p be prime dividing . In this article, we supply some sufficient conditions for G to be p-nilpotent (see Theorem 1.2) as an extension of the main theorem of Li et al. (J. Group Theor. 20(1): 185-192, 2017).
Good action on a finite group Ercan, Gülin; Jabara, Enrico (Elsevier BV, 2020-10-01) Let G and A be finite groups with A acting on G by automorphisms. In this paper we introduce the concept of "good action"; namely we say the action of A on G is good, if H = [H, B]C-H (B) for every subgroup B of A and every B-invariant subgroup H of G. This definition allows us to prove a new noncoprime Hall-Higman type theorem.
ON THE NUMBER OF QUADRATIC FORMS HAVING CODIMENSION 2 RADICALS IN CHARACTERISTIC 2 GIVING MAXIMAL/MINIMAL CURVES Özbudak, Ferruh (Informa UK Limited, 2014-09-02) Let F-q be an arbitrary finite field of characteristic 2 and k be an arbitrary even integer. We count the number of quadratic forms having codimension 2 radicals on F-q(k) over F-q such that the corresponding curve is maximal or minimal. This problem is first attempted in [3], in which the number of maximal curves is obtained only for (q, k) = (2, 6) and (q, k) = (2, 8).
The classical involution theorem for groups of finite Morley rank Berkman, A (Elsevier BV, 2001-09-15) This paper gives a partial answer to the Cherlin-Zil'ber Conjecture, which states that every infinite simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field. The classification of the generic case of tame groups of odd type follows from the main result of this work, which is an analogue of Aschbacher's Classical Involution Theorem for finite simple groups. (C) 2001 Academic Press.
Invariant subspaces for banach space operators with a multiply connected spectrum Yavuz, Onur (Springer Science and Business Media LLC, 2007-07-01) We consider a multiply connected domain Omega = D \U (n)(j= 1) (B) over bar(lambda(j), r(j)) where D denotes the unit disk and (B) over bar(lambda(j), r(j)) subset of D denotes the closed disk centered at lambda(j) epsilon D with radius r(j) for j = 1,..., n. We show that if T is a bounded linear operator on a Banach space X whose spectrum contains delta Omega and does not contain the points lambda(1),lambda(2),...,lambda(n), and the operators T and r(j)( T -lambda I-j)(-1) are polynomially bounded, then th...

Citation Formats

E. M. Turkan, “Implications of the index of a fixed point subgroup,” RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, pp. 1–7, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63724.