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Proofs of some geometric conjectures on the power sum congruence modulo a prime [PDF]
Notes on Number Theory and Discrete MathematicsThe main purpose of this paper is to verify the geometric conjectures of Mustonen (2022) concerning the solutions and the number of solutions of the congruence xⁿ+yⁿ≡0 (mod p), where p is a prime. For p>2, the nontrivial solutions lie on the "lines" y≡cx
Pentti Haukkanen
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Planarity of Inclusion Graph of Cyclic Subgroups of Finite Group [PDF]
Mathematics Interdisciplinary Research, 2020 Let G be a finite group. The inclusion graph of cyclic subgroups of G, Ic(G), is the (undirected) graph with vertices of all cyclic subgroups of G, and two distinct cyclic subgroups ⟨a⟩ and ⟨b⟩, are adjacent if and only if ⟨a⟩ ⊂ ⟨b⟩ or ⟨b⟩ ⊂ ⟨a⟩. In this
Zahra Garibbolooki, Sayyed Heidar Jafari
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Covering certain Wreath Products with Proper Subgroups [PDF]
, 2010 For a non-cyclic finite group $X$ let $\sigma(X)$ be the least number of proper subgroups of $X$ whose union is $X$. Precise formulas or estimates are given for $\sigma(S \wr C_{m})$ for certain nonabelian finite simple groups $S$ where $C_m$ is a cyclic
Garonzi, Martino, Maroti, Attila
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Cartesian symmetry classes associated with certain subgroups of $S_m$ [PDF]
International Journal of Group TheoryIn this paper, the problem existing $O$-basis for Cartesian symmetry classes is discussed. The dimensions of Cartesian symmetry classes associated with a cyclic subgroup of the symmetric group $S_m$ (generated by a product of disjoint cycles) and the ...
Seyyed Sadegh Gholami, Yousef Zamani
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Free cyclic submodules in the context of the projective line [PDF]
, 2015 We discuss the free cyclic submodules over an associative ring $R$ with unity. Special attention is paid to those, which are generated by outliers. This paper describes all orbits of such submodules in the ring of lower triangular $3$x$3$ matrices over a
Bartnicka, Edyta, Matras, Andrzej
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New Two-Stage Automorphism Group Decoders for Cyclic Codes
IEEE Access, 2020 Recently, error correcting codes in the erasure channel have drawn great attention for various applications such as distributed storage systems and wireless sensor networks, but many of their decoding algorithms are not practical because they have higher
Chanki Kim, Jong-Seon No
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Non-periodic groups with the restrictions on the norm of cyclic subgroups of non-prime order
Математичні Студії, 2022 One of the main directions in group theory is the study of the impact of characteristic subgroups on the structure of the whole group. Such characteristic subgroups include different $\Sigma$-norms of a group.
M. Drushlyak, T. Lukashova
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A group sum inequality and its application to power graphs [PDF]
, 2014 Let $G$ be a finite group of order $n$, and let $C_n$ be the cyclic group of order $n$. We show that $\sum_{g \in C_n} \phi(\mathrm{o}(g))\geq \sum_{g \in G} \phi(\mathrm{o}(g))$, with equality if and only if $G$ is isomorphic to $C_n$. As an application,
Curtin, Brian, Pourgholi, Gholam Reza
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Cyclically separated groups [PDF]
Bulletin of the Australian Mathematical Society, 1982 We call a group G cyclically separated if for any given cyclic subgroup B in G and subgroup A of finite index in B, there exists a normal subgroup N of G of finite index such that N ∩ B = A. This is equivalent to saying that for each element x ∈ G and integer n ≥ 1 dividing the order o(x) of x, there exists a normal subgroup N of G of finite index such
Hartley, Brian +2 more
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Uniform cyclic group factorizations of finite groups
Communications in Algebra, 2023 In this paper, we introduce a kind of decomposition of a finite group called a uniform group factorization, as a generalization of exact factorizations of a finite group. A group $G$ is said to admit a uniform group factorization if there exist subgroups $H_1, H_2, \ldots, H_k$ such that $G = H_1 H_2 \cdots H_k$ and the number of ways to represent any ...
Kazuki Kanai +3 more
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