a $p$-group $g$ is called a $mathcal{cac}$-$p$-group if $c_g(h)/h$ is ‎cyclic for every non-cyclic abelian subgroup $h$ in $g$ with $hnleq‎ ‎z(g)$‎. ‎in this paper‎, ‎we give a complete classification of‎ ‎finite $mathcal{cac}$-$p$-groups‎.

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

Generally, phone recognition system contains only a single phone recognizer. The phone set and speech representation for a recognizer are optimized for a particular task. This paper studies the effect of phone sets and speech representations for TIMIT phone recognition task. Two phone sets (TIMIT original phone set and 39 classical phone set) and two speech representations (MFCC-based and PLP-b...

We present in this paper a neural-like membrane system solving the SAT problem in linear time. These neural P systems are nets of cells working with multisets. Each cell has a finite state memory, processes multisets of symbol-impulses, and can send impulses ("excitations" ) to the neighboring cells. The maximal mode of rules application and the replicative mode of communication between cells a...

The finite logarithm was introduced by Kontsevich (under the name “The 1 1 2 logarithm”) in [Kon]. The finite logarithm is the case n = 1 of the n-th polylogarithm lin ∈ Z/p[z] defined by lin(z) = ∑p−1 k=1 z /k. In loc. cit. Kontsevich proved that the finite logarithm satisfies a 4-term functional equation, known as the fundamental equation of information theory. The same functional equation is...