Groups whose same-order types are arithmetic progressions

نویسندگان

چکیده

The same-order type τe(G) of a finite group G is set formed the sizes equivalence classes containing same order elements G. In this paper, we study an arithmetical property set. More exactly, outline some results on classification and existence groups whose types are arithmetic progressions 3 or 4 elements, latter being maximum size such sequence.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Classification of finite simple groups whose Sylow 3-subgroups are of order 9

In this paper, without using the classification of finite simple groups, we determine the structure of  finite simple groups whose Sylow 3-subgroups are of the order 9. More precisely, we classify finite simple groups whose Sylow 3-subgroups are elementary abelian of order 9.

متن کامل

Rainbow Arithmetic Progressions in Finite Abelian Groups

For positive integers n and k, the anti-van der Waerden number of Zn, denoted by aw(Zn, k), is the minimum number of colors needed to color the elements of the cyclic group of order n and guarantee there is a rainbow arithmetic progression of length k. Butler et al. showed a reduction formula for aw(Zn, 3) = 3 in terms of the prime divisors of n. In this paper, we analagously define the anti-va...

متن کامل

Finite groups all of whose proper centralizers are cyclic

‎A finite group $G$ is called a $CC$-group ($Gin CC$) if the centralizer of each noncentral element of $G$ is cyclic‎. ‎In this article we determine all finite $CC$-groups.

متن کامل

On rainbow 4-term arithmetic progressions

{sl Let $[n]={1,dots, n}$ be colored in $k$ colors. A rainbow AP$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. Conlon, Jungi'{c} and Radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow AP(4) free, when $n$ is even. Based on their construction, we show that such a coloring of $[4n]$...

متن کامل

Arithmetic progressions in multiplicative groups of finite fields

Let G be a multiplicative subgroup of the prime field Fp of size |G| > p1−κ and r an arbitrarily fixed positive integer. Assuming κ = κ(r) > 0 and p large enough, it is shown that any proportional subset A ⊂ G contains non-trivial arithmetic progressions of length r. The main ingredient is the Szemerédi-Green-Tao theorem. Introduction. We denote by Fp the prime field with p elements and Fp its ...

متن کامل

ذخیره 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: Quaestiones Mathematicae

سال: 2021

ISSN: ['1727-933X', '1607-3606']

DOI: https://doi.org/10.2989/16073606.2021.1942288