The modular isomorphism problem for the groups of order 512

نویسندگان

  • BETTINA EICK
  • ALEXANDER KONOVALOV
چکیده

For a prime p let G be a finite p-group and K a field of characteristic p. The Modular Isomorphism Problem (MIP) asks whether the modular group algebra KG determines the isomorphism type of G. We briefly survey the history of this problem and report on our computer-aided verification of the Modular Isomorphism Problem for the groups of order 512 and the field K with 2 elements.

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

The Restricted Isomorphism Problem for Metacyclic Restricted Lie Algebras

Let L be a restricted Lie algebra with the restricted enveloping algebra u(L) over a perfect field of positive characteristic p. The restricted isomorphism problem asks what invariants of L are determined by u(L). This problem is the analogue of the modular isomorphism problem for finite p-groups. Bagiński and Sandling have given a positive answer to the modular isomorphism problem for metacycl...

متن کامل

Cohomological Uniqueness, Massey Products and the Modular Isomorphism Problem for 2-groups of Maximal Nilpotency Class

Let G be a finite 2-group of maximal nilpotency class, and let BG be its classifying space. We prove that iterated Massey products inH∗(BG;F2) do characterize the homotopy type of BG among 2-complete spaces with the same cohomological structure. As a consequence we get an alternative proof of the modular isomorphism problem for 2-groups of maximal nilpotency class.

متن کامل

Positive Cone in $p$-Operator Projective Tensor Product of Fig`a-Talamanca-Herz Algebras

In this paper we define an order structure on the $p$-operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.

متن کامل

Supplementary Notes for Math 512 (version 0.15)

1. Even periodic ring theories and formal group laws 1 2. Formal groups 5 3. Geometry of formal groups 8 4. Heights of formal groups 12 5. Homology of Z× BU and related spaces 15 6. The Thom isomorphism 19 7. Elliptic spectra 24 8. The generalized Weierstrass equation 25 9. Modular forms 29 10. Elliptic curves and the group structure 30 11. Weierstrass parameters and Thom spectrum of ΩU(4) 33 1...

متن کامل

EFFICIENT SIMULATION FOR OPTIMIZATION OF TOPOLOGY, SHAPE AND SIZE OF MODULAR TRUSS STRUCTURES

The prevalent strategy in the topology optimization phase is to select a subset of members existing in an excessively connected truss, called Ground Structure, such that the overall weight or cost is minimized. Although finding a good topology significantly reduces the overall cost, excessive growth of the size of topology space combined with existence of varied types of design variables challe...

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 2010