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A Note on Groups of Ree Type [PDF]
Canadian Mathematical Bulletin, 1973 The nonsolvable R-groups as defined by Walter [3] are groups of orders (q3+l)q3(q — 1), q = 32n+1, n ≥ 0. These are the groups of Ree type discussed by Ward [4] together with the Ree group R(3) of order 28.27.2. The R-group with parameter q has a doubly transitive representation of degree q3+1 but in this note we will prove that it cannot contain a ...
Peter Lorimer
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Algebra and Logic, 1985
On the basis of a description of the maximal subgroups of finite Ree groups \({}^ 2G_ 2(3^ n)\) the authors prove that for every infinite family K of finite Ree groups the free group with two generators is residually a K-group.
Levchuk, V. M., Nuzhin, Ya. N.
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On the basis of a description of the maximal subgroups of finite Ree groups \({}^ 2G_ 2(3^ n)\) the authors prove that for every infinite family K of finite Ree groups the free group with two generators is residually a K-group.
Levchuk, V. M., Nuzhin, Ya. N.
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Euler-Hall functions on Ree groups
Siberian Mathematical Journal, 2013For every nonabelian simple group \(G\) and for each natural \(n\geq 2\), there exists a greatest number \(d=d_n(G)\) such that the direct power \(G^d\) is generated by \(n\) elements. The authors compute the precise value of \(d_2(G)\) when \(G\) is a finite simple Ree group of type \(^2G_2\).
Levchuk, D. V., Ushakov, Yu. Yu.
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Canonical Modules and Class Groups of Rees-Like Algebras
Michigan Mathematical Journal, 2023Let \(S = k[x_1,\ldots,x_n]\) the polynomial ring in \(n\) variables over the field \(k\). For a homogeneous ideal \(I = (f_1,\ldots,f_m)\) the Rees-like algebra is defined by \(S[It, t^2] \subset S[t]\), where \(t\) is a variable. Let \(T = S[y_1,\ldots,y_m,z]\) be the non-standard graded polynomial ring with a natural map \(T \to S[It, t^2]\), where ...
Mantero, Paolo +2 more
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Exponential Sums, Ree Groups and Suzuki Groups: Conjectures
Experimental Mathematics, 2017Inspired by work of Gross, we exhibit rigid local systems on the affine line whose monodromy groups we conjecture to be the Suzuki and Ree groups, in characteristics 2 and 3 respectively.
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Primitive Prime Divisors of Orders of Suzuki–Ree Groups
Algebra and Logic, 2023A primitive prime divisor of \(q^{m}-1\), where \(q\) and \(m\) are integers larger than 1, is a prime that divides \(q^{m}-1\) and does not divide \(q^{i}-1\) for all \(1 \leq i < m\). From a result by \textit{K. Zsigmondy} [Monatsh. f. Math. 3, 265--284 (1892; JFM 24.0176.02)] primitive prime divisors exist except in the following two cases (a) \(m=2\
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Moufang Octagons and the Ree Groups of Type 2 F 4
American Journal of Mathematics, 1983info:eu-repo/semantics ...
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A new characterization of Suzuki-Ree group
Science in China Series A: Mathematics, 1997Let \(G\) be a finite group and \(\pi_i\) (\(1\leq i\leq t\)) are all prime graph components of \(G\). Then \(|G|\) can be expressed as a product of coprime positive integers \(m_1,\dots,m_t\), where \(\pi(m_i)=\pi_i\) (\(1\leq i\leq t\)). The set \(\{m_1,\dots,m_t\}\) is denoted by \(OC(G)\).
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Encryption scheme based on small Ree groups
2021 7th International Conference on Computer Technology Applications, 2021Gennady Khalimov +3 more
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