PROOF OF THE PRIME POWER CONJECTURE FOR PROJECTIVE PLANES OF ORDER n WITH ABELIAN COLLINEATION GROUPS OF ORDER n

نویسندگان

  • AART BLOKHUIS
  • DIETER JUNGNICKEL
  • Stephen D. Smith
چکیده

Let G be an abelian collineation group of order n2 of a projective plane of order n. We show that n must be a prime power, and that the p-rank of G is at least b+ 1 if n = pb for an odd prime p.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Another case of the prime power conjecture for finite projective planes

Let G be an abelian collineation group of order nðn 1Þ of a projective plane of order n. We show that n must be power of a prime p and that the p-part of G is elementary abelian.

متن کامل

New characterization of some linear ‎groups‎

‎There are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{Z}_{2}$ or $mathbb{Z}_{15}$. Still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of Sylow $p$-subgroups for each prime $p$, etc. In this...

متن کامل

Cyclic affine planes and Paley difference sets

Arasu, K.T. and A. Pott, Cyclic affine planes and Paley difference sets, Discrete Mathematics 106/107 (1992) 19-23. The existence of a cyclic affine plane implies the existence of a Paley type difference set. We use the existence of this difference set to give the following condition on the existence of cyclic affine planes of order n: If n 8 mod 16 then n 1 must be a prime. We discuss the stru...

متن کامل

On projective planes of order 12 with a collineation group of order 9

In this paper, we prove that if π is a projective plane of order 12 admitting a collineation group G of order 9, then G is an elementary abelian group and is not planar.

متن کامل

2-quasirecognizability of the simple groups B_n(p) and C_n(p) by prime graph

Let G be a finite group and let $GK(G)$ be the prime graph of G. We assume that $n$ is an odd number. In this paper, we show that if $GK(G)=GK(B_n(p))$, where $ngeq 9$ and $pin {3,5,7}$, then G has a unique nonabelian composition factor isomorphic to $B_n(p)$ or $C_n(p)$ . As consequences of our result, $B_n(p)$ is quasirecognizable by its spectrum and also by a new proof, the ...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2001