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On some measures of complexity of finite Abelian groups by Vadim V. Kochergin is a Computer Science article available to read on EtoBox.

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Let a finite Abelian multiplicative group be specified by the basis = { 1 , 2 , . . . , }, that is, the group is decomposed into a direct product of cyclic subgroups generated by the elements of the set : The complexity ( ; ) of an element of the group in the basis is defined as the minimum number of multiplication operations required to compute the element given the basis (it is allowed to use the results of intermediate computations many times). Let ( , ) = max ∈ ( ; ), ( ) = max ( , ), ( ) = min ( , ), ( ) = max : | |≤ ( ), ( ) = max : | |≤ ( ), av ( ) = ∑ : | |= ( ) / ( ), av ( ) = ∑ : | |= ( ) / ( ), where ( ) is the number of Abelian groups of order . In this work the asymptotic estimates for the quantities ( , ), ( ), ( ), av ( ), and av ( ) are established.

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Author

Vadim V. Kochergin

Publisher

Walter de Gruyter GmbH

Published

2017

Language

EN

Field

Computer Science (Physical Sciences)