Results 61 to 70 of about 104,175 (189)
Algebras and Dihedral Defect Groups
Proceedings of the London Mathematical Society, 1987 Let F be an algebraically closed field of characteristic 2, and let G be a finite group. Let B be a block of the group algebra FG with dihedral defect group D of order \(2^ n\). It has been proved by \textit{R. Brauer} [Symp. Math. 13, 367-393 (1974; Zbl 0288.20010)] that B has either 1, 2 or 3 simple modules.
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On Order Prime Divisor Graphs of Finite Groups
Discussiones Mathematicae - General Algebra and Applications, 2021 The order prime divisor graph 𝒫𝒟(G) of a finite group G is a simple graph whose vertex set is G and two vertices a, b ∈ G are adjacent if and only if either ab = e or o(ab) is some prime number, where e is the identity element of the group G and o(x ...
Sen Mridul K. +2 more
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Dihedral Group Frames which are Maximally Robust to Erasures [PDF]
, 2014 Let $n$ be a natural number larger than two. Let $D_{2n}=\langle r,s : r^{n}=s^{2}=e, srs=r^{n-1} \rangle$ be the Dihedral group, and $\kappa $ an $n$-dimensional unitary representation of $D_{2n}$ acting in $\mathbb{C}^n$ as follows. $(\kappa (r)v)(j)=v(
Oussa, Vignon
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Virtually free finite-normal-subgroup-free groups are strongly verbally closed
, 2018 Any virtually free group $H$ containing no non-trivial finite normal subgroup (e.g., the infinite dihedral group) is a retract of any finitely generated group containing $H$ as a verbally closed subgroup.Comment: 6 pages. V2: minor corrections.
Klyachko, Anton A. +2 more
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Journal of Algebra, 1979 AbstractThis paper determines much of the structure of blocks whose defect group is dihedral, semidihedral or generalised quaternion and which have either one or two simple modular representations (Brauer characters). It is shown that in the above circumstances there is only a very small number of possibilities for the Cartan matrix, decomposition ...
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Some properties of Square element graphs over semigroups
AKCE International Journal of Graphs and Combinatorics, 2020 The Square element graph over a semigroup is a simple undirected graph whose vertex set consists precisely of all the non-zero elements of , and two vertices are adjacent if and only if either or belongs to the set , where 1 is the identity of the ...
Bijon Biswas +3 more
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Discrete Group Actions on Digital Objects and Fixed Point Sets by Isok(·)-Actions
Mathematics, 2021 Given a digital image (or digital object) (X,k),X⊂Zn, this paper initially establishes a group structure of the set of self-k-isomorphisms of (X,k) with the function composition, denoted by Isok(X) or Autk(X).
Sang-Eon Han
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On the Spectra of Commuting and Non Commuting Graph on Dihedral Group
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2017 Study about spectra of graph has became interesting work as well as study about commuting and non commuting graph of a group or a ring. But the study about spectra of commuting and non commuting graph of dihedral group has not been done yet.
Abdussakir Abdussakir +2 more
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MathematicsThe HX-groups represent a generalization of the group notion. The Chinese mathematicians Mi Honghai and Li Honxing analyzed this theory. Starting with a group (G,·), they constructed another group (G,∗)⊂P∗(G), where P∗(G) is the set of non-empty subsets ...
Andromeda Pătraşcu Sonea +1 more
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Words and polynomial invariants of finite groups in non-commutative variables [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Let $V$ be a complex vector space with basis $\{x_1,x_2,\ldots,x_n\}$ and $G$ be a finite subgroup of $GL(V)$. The tensor algebra $T(V)$ over the complex is isomorphic to the polynomials in the non-commutative variables $x_1, x_2, \ldots, x_n$ with ...
Anouk Bergeron-Brlek +2 more
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