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The Annals of Mathematics, 1955
odd order are soluble. We shall use the term involution for a group element of order 2. If m is the total number of involutions of 65 and if we set n = g/m, the same method shows that 65 contains a normal subgroup V distinct from 5 such that the index of V is either 2 or is less than [n(n + 2)/2]!
Brauer, Richard, Fowler, K. A.
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odd order are soluble. We shall use the term involution for a group element of order 2. If m is the total number of involutions of 65 and if we set n = g/m, the same method shows that 65 contains a normal subgroup V distinct from 5 such that the index of V is either 2 or is less than [n(n + 2)/2]!
Brauer, Richard, Fowler, K. A.
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The Largest Group Contained in the Order Completion of a Totally Ordered Group
p-Adic Numbers, Ultrametric Analysis and Applications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Muci, Adrialy, Olivos, Elena
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Algebra and Logic, 2003
\textit{P. Dehornoy} [J. Knot Theory Ramifications 4, No. 1, 33-79 (1995; Zbl 0873.20030)] has proved that the braid group \(B(n)\) possesses a right linear order, i.e., a right linear order such that \(x\leq y\) implies \(xz\leq yz\) for any \(x,y,z\in B(n)\).
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\textit{P. Dehornoy} [J. Knot Theory Ramifications 4, No. 1, 33-79 (1995; Zbl 0873.20030)] has proved that the braid group \(B(n)\) possesses a right linear order, i.e., a right linear order such that \(x\leq y\) implies \(xz\leq yz\) for any \(x,y,z\in B(n)\).
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Canadian Journal of Mathematics, 1972
A group G is right-ordered if it can be totally ordered so that for any a, b, c in G, a < b implies that ac < bc. Right-ordered groups, considered as order preserving automorphisms of ordered sets, were studied by Cohn in [4]; but the first
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A group G is right-ordered if it can be totally ordered so that for any a, b, c in G, a < b implies that ac < bc. Right-ordered groups, considered as order preserving automorphisms of ordered sets, were studied by Cohn in [4]; but the first
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On determining the order of a group
Proceedings of the third ACM symposium on Symbolic and algebraic computation - SYMSAC '76, 1976The recent past has seen a proliferation of algorithms designed to carry out a variety of calculations with groups. Chief among these is a family of algorithms for determining the order of a group. While computing the order of a group is often of great interest in itself, the importance of many of these algorithms lies in the fact that they also ...
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1999
Recent progress in computational representation theory is surveyed. As an application of some methods for constructing ordinary character tables Brauer pairs among 2-groups of order up to 28 are determined. Furthermore the present status of the library of the tables of marks for simple groups which is available in GAPis described.
Bettina Eick, Eamonn A. O'Brien
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Recent progress in computational representation theory is surveyed. As an application of some methods for constructing ordinary character tables Brauer pairs among 2-groups of order up to 28 are determined. Furthermore the present status of the library of the tables of marks for simple groups which is available in GAPis described.
Bettina Eick, Eamonn A. O'Brien
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ON THE ORDERS OF AUTOMORPHISM GROUPS OF FINITE GROUPS
Bulletin of the London Mathematical Society, 2005Summary: In the Kourovka notebook, Deaconescu asks whether \(|\Aut G|\geq\varphi(|G|)\) for all finite groups \(G\), where \(\varphi\) denotes the Euler totient function, and whether \(G\) is cyclic whenever \(|\Aut G|=\varphi(|G|)\). Both questions are answered in the negative in this paper.
Bray, John N., Wilson, Robert A.
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