Geodesic
On one representation of elements of finite $2$-groups in the form of Boolean vectors
Prikladnaya Diskretnaya Matematika. Supplement, no. 16 (2023), pp. 129-131

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In this paper, we propose a way to represent elements of finite $2$-groups as Boolean vectors. Let $G$ be some finite (Burnside) 2-group and its order is $2^k$. In this case, each element of the group will be represented by a unique Boolean (bit) vector of dimension $k$. To calculate the product of two elements, we use analogues of Hall polynomials but now instead of multiplication and addition over the field $\mathbb{Z}_2$ we use the equivalent Boolean (bitwise) operations “and”, as well as “exclusive or”. Note that operations on bits are much faster on a computer than on integer or string data types. For problems requiring the calculation of a large number of products of group elements the method will dramatically reduce the running time of computer programs.
Mots-clés : $2$-group
Keywords: Boolean vector, Hall polynomials. 
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     author = {A. A. Kuznetsov and A. S. Kuznetsova},
     title = {On one representation of elements of finite $2$-groups in the form of {Boolean} vectors},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {129--131},
     publisher = {mathdoc},
     number = {16},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2023_16_a32/}
}
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A. A. Kuznetsov; A. S. Kuznetsova. On one representation of elements of finite $2$-groups in the form of Boolean vectors. Prikladnaya Diskretnaya Matematika. Supplement, no. 16 (2023), pp. 129-131. http://geodesic.mathdoc.fr/item/PDMA_2023_16_a32/