On isomorphism testing of a class of 2-Nilpotent groups
Journal of Computer and System Sciences
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
Journal of Computer and System Sciences
On some computational problems in finite Abelian groups
Mathematics of Computation
A space efficient algorithm for group structure computation
Mathematics of Computation
Introduction to Algorithms
On the nlog n isomorphism technique (A Preliminary Report)
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Linear time algorithms for Abelian group isomorphism and related problems
Journal of Computer and System Sciences
An algorithm for computing a basis of a finite abelian group
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Linear time algorithms for the basis of abelian groups
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
| Hi-index | 5.23 |
It is well known that every finite abelian group G can be represented as a direct product of cyclic groups: G@?G"1xG"2x...xG"t, where each G"i is a cyclic group of order p^j for some prime p and integer j=1. If a"i generates the cyclic group of G"i, i=1,2,...,t, then the elements a"1,a"2,...,a"t are called a basis of G. We show a randomized algorithm such that given a set of generators M={x"1,...,x"k} for an abelian group G and the prime factorization of order ord(x"i)(i=1,...,k), it computes a basis of G in O(|M|(logn)^2+@?"i"="1^tn"ip"i^n^"^i^/^2) time, where n=|G| has prime factorization p"1^n^"^1p"2^n^"^2...p"t^n^"^t (which is not a part of input). This generalizes Buchmann and Schmidt's algorithm that takes O(|M||G|) time. In another model, all elements in an abelian group are put into a list as a part of input. We obtain an O(n) time deterministic algorithm and a sublinear time randomized algorithm for computing a basis of an abelian group.