Search results for "Elementary abelian group"
showing 10 items of 11 documents
Kurzweil-Henstock type integral on zero-dimensional group and some of its application
2008
A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case.
Perron type integral on compact zero-dimensional Abelian groups
2008
Perron and Henstock type integrals defined directly on a compact zero-dimensional Abelian group are studied. It is proved that the considered Perron type integral defined by continuous majorants and minorants is equivalent to the integral defined in the same way, but without assumption on continuity of majorants and minorants.
Hyper-abelian groups with finite co-central rank
2004
AbstractA group G has finite co-central rank s if there exists a least non-negative integer s such that every finitely generated subgroup H can be generated by at most s elements modulo the centre of H. The investigation of such groups has been started in [J.P. Sysak, A. Tresch, J. Group Theory 4 (2001) 325]. It is proved that hyper-abelian groups with finite co-central rank are locally soluble. The interplay between the Prüfer rank condition, the condition of having finite abelian section rank and the finite co-central rank condition is studied. As one result, a hyper-abelian group G with finite co-central rank has an ascending series with abelian factors of finite rank and every chief fac…
Transitive permutation groups in which all derangements are involutions
2006
AbstractLet G be a transitive permutation group in which all derangements are involutions. We prove that G is either an elementary abelian 2-group or is a Frobenius group having an elementary abelian 2-group as kernel. We also consider the analogous problem for abstract groups, and we classify groups G with a proper subgroup H such that every element of G not conjugate to an element of H is an involution.
Abelian gradings on upper-triangular matrices
2003
Let G be an arbitrary finite abelian group. We describe all possible G-gradings on an upper-triangular matrix algebra over an algebraically closed field of characteristic zero.
Hybrid bases for varieties of semigroups
2003
We consider the lower part of the lattice of varieties of semigroups. We present finite bases of hybrid identities for the varieties of normal bands, commutative bands and abelian groups of finite exponent. The variety A n,0 of abelian groups provides an example of a variety which has no finite base of hyperidentities (cf. [12]) but has a finite base of hybrid identities.
Identities of PI-Algebras Graded by a Finite Abelian Group
2011
We consider associative PI-algebras over an algebraically closed field of zero characteristic graded by a finite abelian group G. It is proved that in this case the ideal of graded identities of a G-graded finitely generated PI-algebra coincides with the ideal of graded identities of some finite dimensional G-graded algebra. This implies that the ideal of G-graded identities of any (not necessary finitely generated) G-graded PI-algebra coincides with the ideal of G-graded identities of the Grassmann envelope of a finite dimensional (G × ℤ2)-graded algebra, and is finitely generated as GT-ideal. Similar results take place for ideals of identities with automorphisms.
Algorithms for Computing Abelian Periods of Words
2012
Constantinescu and Ilie (Bulletin EATCS 89, 167--170, 2006) introduced the notion of an \emph{Abelian period} of a word. A word of length $n$ over an alphabet of size $\sigma$ can have $\Theta(n^{2})$ distinct Abelian periods. The Brute-Force algorithm computes all the Abelian periods of a word in time $O(n^2 \times \sigma)$ using $O(n \times \sigma)$ space. We present an off-line algorithm based on a $\sel$ function having the same worst-case theoretical complexity as the Brute-Force one, but outperforming it in practice. We then present on-line algorithms that also enable to compute all the Abelian periods of all the prefixes of $w$.
A note on easy and efficient computation of full abelian periods of a word
2016
Constantinescu and Ilie (Bulletin of the EATCS 89, 167-170, 2006) introduced the idea of an Abelian period with head and tail of a finite word. An Abelian period is called full if both the head and the tail are empty. We present a simple and easy-to-implement $O(n\log\log n)$-time algorithm for computing all the full Abelian periods of a word of length $n$ over a constant-size alphabet. Experiments show that our algorithm significantly outperforms the $O(n)$ algorithm proposed by Kociumaka et al. (Proc. of STACS, 245-256, 2013) for the same problem.
Fast computation of abelian runs
2016
Given a word $w$ and a Parikh vector $\mathcal{P}$, an abelian run of period $\mathcal{P}$ in $w$ is a maximal occurrence of a substring of $w$ having abelian period $\mathcal{P}$. Our main result is an online algorithm that, given a word $w$ of length $n$ over an alphabet of cardinality $\sigma$ and a Parikh vector $\mathcal{P}$, returns all the abelian runs of period $\mathcal{P}$ in $w$ in time $O(n)$ and space $O(\sigma+p)$, where $p$ is the norm of $\mathcal{P}$, i.e., the sum of its components. We also present an online algorithm that computes all the abelian runs with periods of norm $p$ in $w$ in time $O(np)$, for any given norm $p$. Finally, we give an $O(n^2)$-time offline randomi…