DSpace Community: Научный журналНаучный журналhttp://hdl.handle.net/123456789/152020-09-19T23:31:01Z2020-09-19T23:31:01ZOn one class of algebrasZhuchok, Y. V.http://hdl.handle.net/123456789/49312020-02-15T03:02:37Z2014-01-01T00:00:00ZTitle: On one class of algebras
Authors: Zhuchok, Y. V.
Abstract: In this paper a g-dimonoid which is isomorphic to the free g-dimonoid is given and a free n-nilpotent g-dimonoid is constructed. We also present the least n-nilpotent congruence on a free g-dimonoid and give numerous examples of g-dimonoids.
Description: Zhuchok Y. V. On one class of algebra / Y. V. Zhuchok // Algebra and Discrete Mathematics. - 2014. - № 2 (18). - Рp. 306–3202014-01-01T00:00:00ZOn new multivariate cryptosystems with nonlinearity gapUstimenko, V.http://hdl.handle.net/123456789/46812020-01-23T12:57:00Z2017-01-01T00:00:00ZTitle: On new multivariate cryptosystems with nonlinearity gap
Authors: Ustimenko, V.
Abstract: The pair of families of bijective multivariate maps
of kind Fn and Fn
−1
on affine space Kn over finite commutative ring
K given in their standard forms has a nonlinearity gap if the degree
of Fn is bounded from above by independent constant d and degree
of F
−1
is bounded from below by c
n, c > 1. We introduce examples
of such pairs with invertible decomposition Fn = G1
nG2
n . . . Gk
n,
i.e. the decomposition which allows to compute the value of F
n−1
in given point p = (p1, p2, . . . , pn) in a polynomial time O(n
2
).
The pair of families Fn, F
′
n of nonbijective polynomial maps of
affine space Kn such that composition FnF
′
n leaves each element
of K∗n
unchanged such that deg(Fn) is bounded by independent
constant but deg(F
′
n
) is of an exponential size and there is a decom-
position G1
nG2
n . . . Gk
n of Fn which allows to compute the reimage
of vector from F(K∗n
) in time 0(n
2
). We introduce examples of
such families in cases of rings K = Fq and K = Zm.
Description: Ustimenko V. On new multivariate cryptosystems with nonlinearity gap / V. Ustimenko // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 2. - Рp. 331 - 3482017-01-01T00:00:00ZOn groups with biprimary subgroups of even orderSokhor, I.http://hdl.handle.net/123456789/46782020-01-23T12:57:02Z2017-01-01T00:00:00ZTitle: On groups with biprimary subgroups of even order
Authors: Sokhor, I.
Abstract: We investigate groups in which maximal sub-
groups of even order are primary or biprimary. We also research
soluble groups with restriction on a number of prime devisors of some
proper subgroup orders. We give applications of received results to
cofactors of proper subgroups.
Description: Sokhor I. On groups with biprimary subgroups of even order / I.Sokhor // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 2. - Рp. 312 - 3302017-01-01T00:00:00ZA note on Hall S-permutably embedded subgroups of finite groupsSinitsa, D.A.http://hdl.handle.net/123456789/46752020-01-23T12:56:25Z2017-01-01T00:00:00ZTitle: A note on Hall S-permutably embedded subgroups of finite groups
Authors: Sinitsa, D.A.
Abstract: Let G be a finite group. Recall that a subgroup A
of G is said to permute with a subgroup B if AB = BA. A subgroup
A of G is said to be S-quasinormal or S-permutable in G if A
permutes with all Sylow subgroups of G. Recall also that HsG is
the S-permutable closure of H in G, that is, the intersection of all
such S-permutable subgroups of G which contain H. We say that
H is Hall S-permutably embedded in G if H is a Hall subgroup of
the S-permutable closure HsG of H in G.
We prove that the following conditions are equivalent: (1) every
subgroup of G is Hall S-permutably embedded in G; (2) the nilpotent
residual GN of G is a Hall cyclic of square-free order subgroup of
G; (3) G = D ⋊ M is a split extension of a cyclic subgroup D of
square-free order by a nilpotent group M, where M and D are both
Hall subgroups of G.
Description: Sinitsa D.A. A note on Hall S-permutably embedded subgroups of finite groups / D.A.Sinitsa // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 2. - Рp.305- 3112017-01-01T00:00:00Z