We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
On some measures of complexity of finite Abelian groups.
- Authors
Kochergin, Vadim V.
- Abstract
Let a finite Abelian multiplicative group G be specified by the basis B = {a1, a2, . . . , aq} that is, the group G is decomposed into a direct product of cyclic subgroups generated by the elements of the set B: G = ⟨a1⟩ × ⟨a2⟩ × . . . × ⟨aq⟩. The complexity L(g; B) of an element g of the group G in the basis B is defined as the minimum number of multiplication operations required to compute the element g given the basis B (it is allowed to use the results of intermediate computations many times). Let L(G,B) = . . . L(g;B), LM(G) = . . . L (G,B), Lm(G) = . . . L (G,B), M(n) = . . . LM(G), m(n) = . . . Lm(G), Mav(n) = (. . . LM(G))/A(n), mav(n) = (. . . Lm (G))/A(n), where A(n) is the number of Abelian groups of order n. In this work the asymptotic estimates for the quantities L(G,B), M(n), m(n), Mav(n), and mav (n) are established.
- Subjects
GROUP testing; GROUPWARE (Computer software); COMPUTER conferencing; COMPUTER software; WORKFLOW software
- Publication
Discrete Mathematics & Applications, 2017, Vol 27, Issue 2, p81
- ISSN
0924-9265
- Publication type
Article
- DOI
10.1515/dma-2017-0010