Frobenius-like groups as groups of automorphisms

A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Such subgroups and sections are abundant in any nonnilpotent finite group. We discuss several recent results about the properties of a finite group G admitting a Frobenius-like group of automorphisms FH aiming at restrictions on G in terms of CG(H) and focusing mainly on bounds for the Fitting height and related parameters. Earlier such results were obtained for Frobenius groups of automorphisms; new theorems for Frobenius-like groups are based on new representation-theoretic results. Apart from a brief survey, the paper contains the new theorem on almost nilpotency of a finite group admitting a Frobenius-like group of automorphisms with fixed-point-free almost extraspecial kerne

Noncoprime action of a cyclic group

Let $A$ be a finite nilpotent group acting fixed point freely on the finite (solvable) group $G$ by automorphisms. It is conjectured that the nilpotent length of $G$ is bounded above by $\ell(A)$, the number of primes dividing the order of $A$ counted with multiplicities. In the present paper we consider the case $A$ is cyclic and obtain that the nilpotent length of $G$ is at most $2\ell(A)$ if $|G|$ is odd. More generally we prove that the nilpotent length of $G$ is at most $2\ell(A)+ \mathbf{c}(G;A)$ when $G$ is of odd order and $A$ normalizes a Sylow system of $G$ where $\mathbf{c}(G;A)$ denotes the number of trivial $A$-modules appearing in an $A$-composition series of $G$

Fixed-point free action of an abelian group of odd non-squarefree exponent

Let A be a finite group acting fixed-point freely on a finite (solvable) group G. A longstanding conjecture is that if (|G|, |A|) = 1, then the Fitting length of G is bounded by the length of the longest chain of subgroups of A. It is expected that the conjecture is true when the coprimeness condition is replaced by the assumption that A is nilpotent. We establish the conjecture without the coprimeness condition in the case where A is an abelian group whose order is a product of three odd primes and where the Sylow 2-subgroups of G are abelian

112Sn(α, ) 116Te reaksiyonu için astrofiziksel S-faktörlerinin ve reaksiyon hızlarının hesaplanması

Çalışmamızda 112Sn(α,) 116Te reaksiyonunun reaksiyon hızları hesaplanmıştır. Hesaplamalar için TALYS 1.95 kodları kullanılmıştır. Ek olarak, düşük enerjili bölgelerde bir reaksiyon olasılığını açıklayan astrofiziksel S faktörleri elde edildi. Hesaplamalarımızın sonuçları, EXFOR veri tabanından alınan deneysel verilere göre kontrol edildi.In our study, the reaction rates of 112Sn(α, ) 116Te reaction were calculated. TALYS 1.95 codes were used for calculations. In addition, astrophysical S-factors were obtained that explain the probability of a reaction in low-energy regions. The results of our calculations were checked according to experimental data from the EXFOR database

Primary Renal Synovial Sarcoma

Synovial sarcomas are generally deep-seated tumors that most often occur in the proximity of large joints of adolescents and young adults. We describe two cases of primary renal synovial sarcoma that were treated successfully by radical nephrectomy. Synovial sarcoma originating from the kidney is extremely rare and the histogenesis is uncertain. Surgical resection and ifosfamide based chemotherapy are the mainstay for the management of renal synovial sarcoma. Fewer than 40 patients have been described in the English literature. Physicians should be aware of the possibility of malignancy in cystic renal masses and raise the suspicion of synovial sarcoma, especially when patients with renal masses are a young adult