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Inseparable Finite Solvable Groups [PDF]
Transactions of the American Mathematical Society, 1976 A finite group is called inseparable if the only proper normal subgroup over which it splits is the identity element. The E-residual, for the formation E of groups in which all Sylow subgroups are elementary abelian, appears to control the action of splitting.
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Tarski’s problem for solvable groups [PDF]
Proceedings of the American Mathematical Society, 1986 In this paper, we show that the free solvable groups (as well as the free nilpotent groups) of finite rank have different elementary theories (i.e., they do not satisfy the same first order sentences of group theory). This result is obtained using a result in group theory (probably due to Malcev and following immediately from a theorem of Auslander and
Rogers, Pat +2 more
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Undistorted solvable linear groups
Transactions of the American Mathematical Society, 2011 We discuss distortion of solvable linear groups over a locally compact field and provide necessary and sufficient conditions for a subgroup to be undistorted when the field is of characteristic zero.
Abels, Herbert, Alperin, Roger
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Discrete Solvable Matrix Groups [PDF]
Proceedings of the American Mathematical Society, 1960 Let GL(n, R) denote the real general linear group with the usual topology. A subgroup of GL(n, R) will be called an w-matrix group. We will say that a subgroup G of GL(n, R) is a discrete group if it is discrete in the induced topology. If for any group G, [G, G] denotes the commutator subgroup of G, we will say that a group 5 is solvable provided the ...
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Automorphisms of solvable groups [PDF]
Proceedings of the American Mathematical Society, 1962 It is important to note that in both these statements only the existence of integers t(p, n) and m(p) is claimed. The only specific information known is that in(2) =2, m (3) =2, and mi(5) = 3 (see [1 ]) . Even upper bounds for the values of t(p, n) and m(p) are not known to us.
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Solvability of generalized monomial groups [PDF]
Journal of Group Theory, 2010 The solvability of monomial groups is a well-known result in character theory. Certain properties of Artin L-series suggest a generalization of these groups, namely to such groups where every irreducible character has some multiple which is induced from a character phi of U with solvable factor group U/ker(phi).
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Jordan’s theorem for solvable groups [PDF]
Proceedings of the American Mathematical Society, 1970 We show that every finite solvable group of n × n n \times n matrices over the complex numbers has a normal abelian subgroup of index ≦ 2 4 n / 3 − 1
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Journal of Algebra, 1996 Let \(Q\) be a loop and \(M(Q)\) be its multiplication group, i.e. the subgroup of the symmetric group \(S_Q\) generated by all the left and right translations. And moreover, let us assume that there exists a series of subloops of the loop \(Q\) of the form \(1=Q_0\leq Q_1\leq\cdots\leq Q_n=Q\), where \(Q_i\) is a normal subloop in \(Q_{i-1}\) and ...
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2-KNOTS WITH SOLVABLE GROUPS [PDF]
Journal of Knot Theory and Its Ramifications, 2011 We show that fibered 2-knots with closed fiber the Hantzsche–Wendt flat 3-manifold are not reflexive, while every fibered 2-knot with closed fiber a Nil-manifold with base orbifold S(3, 3, 3) is reflexive. We also determine when the knots are amphicheiral or invertible, and give explicit representatives for the possible meridians (up to automorphisms ...
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Quadratic rational solvable groups
Journal of Algebra, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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