منابع مشابه
RANK p − 1 MOD - p H - SPACES
Different constructions by Cooke, Harper and Zabrodsky and by Cohen and Neisendorfer produce torsion free finite p-local H-spaces of rank l < p−1. The first construction goes through when l = p− 1 and we show the second does as well. However, the space produced need not be an H-space. We give a criterion for when an H-space is obtained. In the special case of rank 2 mod-3 H-spaces, we also give...
متن کاملNOTES ON PRIMES P ⌘ 1 mod D AND A P � 1 / D ⌘ 1 mod
Let d > 0 be a squarefree integer and a be an integer, which is not 1 nor a square. Let P(a,d)(x) be the number of primes p x such that p ⌘ 1 mod d and a(p 1)/d ⌘ 1 mod p. Numerical data indicate that the function as approximately equal to a constant multiple of ⇡(x)/(d'(d)) for su ciently large x, where ⇡(x) is the number of primes up to x and '(d) is the Euler-' function. The involved const...
متن کاملOn primitive roots of 1 mod p k, divisors of p ± 1, Wieferich primes, and quadratic analysis mod p 3
On primitive roots of 1 mod p k , divisors of p ± 1, Wieferich primes, and quadratic analysis mod p Abstract Primitive roots of 1 mod p k (k > 2 and odd prime p) are sought, in cyclic units group G k ≡ A k B k mod p k , coprime to p, of order (p − 1)p k−1. 'Core' subgroup A k has order p − 1 independent of precision k, and 'extension' subgroup B k of all p k−1 residues 1 mod p is generated by p...
متن کاملMOD p DECOMPOSITIONS OF THE LOOP SPACES OF COMPACT SYMMETRIC SPACES
We give p-local homotopy decompositions of the loop spaces of compact, simplyconnected symmetric spaces for quasi-regular primes. The factors are spheres, sphere bundles over spheres, and their loop spaces. As an application, upper bounds for the homotopy exponents are determined.
متن کاملTHE MOD p REPRESENTATION THEORY OF p - ADIC GROUPS
Exercise 1 (Maximal compact subgroups of G). A lattice in Qp is a finitelygenerated Zp-submodule of Qp that generates Qp as vector space. In particular, it’s free of rank n. Note that G acts transitively on the set of lattices in Qp . (i) Show that K = StabG(Zp ). (ii) Suppose that K ′ is a compact subgroup of G. Show that K ′ stabilises a lattice. (Hint: show that the K ′-orbit of Zp is finite...
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ژورنال
عنوان ژورنال: Hiroshima Mathematical Journal
سال: 1982
ISSN: 0018-2079
DOI: 10.32917/hmj/1206133758