A note on normal complements in mod $p$ envelopes
نویسندگان
چکیده
منابع مشابه
A Note on Mod and Generalised Mod Classes
We characterise Mod classes in terms of #P functions, where the membership is determined by co-primality or gcd testing of the function value (Theorem 3.1), instead of residue (mod k) testing. Imposing a restriction on the range of the functions gives a characterisation of the intersection of Mod classes (Theorem 3.2). These intersection classes, which we denote by Mod ∩k P , are interesting be...
متن کاملp-divisibility of conjugacy class sizes and normal p-complements
LetN be a normal subgroup of a groupG and let p be a prime. We prove that if the p-part of jx j is a constant for every prime-power order element x 2 N n Z.N /, then N is solvable and has normal p-complement.
متن کاملA Note on Equality of Functional Envelopes
We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in m×n , min(m,n) 6 2, then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit conve...
متن کاملA note on the new basis in the mod 2 Steenrod algebra
The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations, denoted by $Sq^n$, between the cohomology groups with $mathbb{Z}_2$ coefficients of any topological space. Regarding to its vector space structure over $mathbb{Z}_2$, it has many base systems and some of the base systems can also be restricted to its sub algebras. On the contrary, in ...
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 کاملذخیره 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: Proceedings of the American Mathematical Society
سال: 1980
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1980-0560574-4