منابع مشابه
Modules for Elementary Abelian p-groups
Let E ∼= (Z/p)r (r ≥ 2) be an elementary abelian p-group and let k be an algebraically closed field of characteristic p. A finite dimensional kE-module M is said to have constant Jordan type if the restriction of M to every cyclic shifted subgroup of kE has the same Jordan canonical form. I shall begin by discussing theorems and conjectures which restrict the possible Jordan canonical form. The...
متن کاملPseudo-Free Families of Finite Computational Elementary Abelian p-Groups
We initiate the study of (weakly) pseudo-free families of computational elementary abelian pgroups, where p is an arbitrary fixed prime. We restrict ourselves to families of computational elementary abelian p-groups Gd such that for every index d, each element of Gd is represented by a single bit string of length polynomial in the length of d. First, we prove that pseudo-freeness and weak pseud...
متن کاملSolving Linear Constraints in Elementary Abelian p-Groups of Symmetries
Symmetries occur naturally in CSP or SAT problems and are not very difficult to discover, but using them to prune the search space tends to be very challenging. Indeed, this usually requires finding specific elements in a group of symmetries that can be huge, and the problem of their very existence is NP-hard. We formulate such an existence problem as a constraint problem on one variable (the s...
متن کاملElementary Abelian Subgroups in p - Groups of Class 2 THÈSE
All the results in this work concern (finite) p-groups. Chapter 1 is concerned with classifications of some classes of p-groups of class 2 and there are no particularly new results in this chapter, which serves more as an introductory chapter. The “geometric” method we use for these classifications differs however from the standard approach, especially for p-groups of class 2 with cyclic center...
متن کاملp-GROUPS WITH MAXIMAL ELEMENTARY ABELIAN SUBGROUPS OF RANK 2
Let p be an odd prime number and G a finite p-group. We prove that if the rank of G is greater than p, then G has no maximal elementary abelian subgroup of rank 2. It follows that if G has rank greater than p, then the poset E(G) of elementary abelian subgroups of G of rank at least 2 is connected and the torsion-free rank of the group of endotrivial kG-modules is one, for any field k of charac...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1995
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700014866