Cohomology of cyclic groups of prime square order
نویسندگان
چکیده
منابع مشابه
Coinvariants for Modular Representations of Cyclic Groups of Prime Order
We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gröbner basis for the Hilbert ideal and the corresponding monomial basis for the coinvariants. We also describe the decomposition of the coinvariants as a module over the group ring. For one family o...
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Let W be a finite-dimensional Z/p-module over a field, k, of characteristic p. The maximum degree of an indecomposable element of the algebra of invariants, k[W ]Z/p, is called the Noether number of the representation, and is denoted by β(W ). A lower bound for β(W ) is derived, and it is shown that if U is a Z/p submodule of W , then β(U) 6 β(W ). A set of generators, in fact a SAGBI basis, is...
متن کاملThe Noether Numbers for Cyclic Groups of Prime Order
The Noether number of a representation is the largest degree of an element in a minimal homogeneous generating set for the corresponding ring of invariants. We compute the Noether number for an arbitrary representation of a cyclic group of prime order, and as a consequence prove the “2p− 3 conjecture”.
متن کاملAn Uncertainty Principle for Cyclic Groups of Prime Order
Let G be a finite abelian group, and let f : G → C be a complex function on G. The uncertainty principle asserts that the support supp(f) := {x ∈ G : f(x) 6= 0} is related to the support of the Fourier transform f̂ : G → C by the formula |supp(f)||supp(f̂)| ≥ |G| where |X| denotes the cardinality of X. In this note we show that when G is the cyclic group Z/pZ of prime order p, then we may improve...
متن کاملFinite groups with $X$-quasipermutable subgroups of prime power order
Let $H$, $L$ and $X$ be subgroups of a finite group$G$. Then $H$ is said to be $X$-permutable with $L$ if for some$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is emph{$X$-quasipermutable } (emph{$X_{S}$-quasipermutable}, respectively) in $G$ provided $G$ has a subgroup$B$ such that $G=N_{G}(H)B$ and $H$ $X$-permutes with $B$ and with all subgroups (with all Sylowsubgroups, respectively) $...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1964
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1964-11128-9