• Title, Summary, Keyword: solvable group

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A note on M-groups

  • 왕문옥
    • Journal for History of Mathematics
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    • v.12 no.2
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    • pp.143-149
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    • 1999
  • Every finite solvable group is only a subgroup of an M-groups and all M-groups are solvable. Supersolvable group is an M-groups and also subgroups of solvable or supersolvable groups are solvable or supersolvable. But a subgroup of an M-groups need not be an M-groups . It has been studied that whether a normal subgroup or Hall subgroup of an M-groups is an M-groups or not. In this note, we investigate some historical research background on the M-groups and also we give some conditions that a normal subgroup of an M-groups is an M-groups and show that a solvable group is an M-group.

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COMMUTATOR LENGTH OF SOLVABLE GROUPS SATISFYING MAX-N

  • Mehri, Akhavan-Malayeri
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.4
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    • pp.805-812
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    • 2006
  • In this paper we find a suitable bound for the number of commutators which is required to express every element of the derived group of a solvable group satisfying the maximal condition for normal subgroups. The precise formulas for expressing every element of the derived group to the minimal number of commutators are given.

A NOTE ON PRIMITIVE SUBGROUPS OF FINITE SOLVABLE GROUPS

  • He, Xuanli;Qiao, Shouhong;Wang, Yanming
    • Communications of the Korean Mathematical Society
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    • v.28 no.1
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    • pp.55-62
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    • 2013
  • In [5], Johnson introduced the primitivity of subgroups and proved that a finite group G is supersolvable if every primitive subgroup of G has a prime power index in G. In that paper, he also posed an interesting problem: what a group looks like if all of its primitive subgroups are maximal. In this note, we give the detail structure of such groups in solvable case. Finally, we use the primitivity of some subgroups to characterize T-group and the solvable $PST_0$-groups.

Stable Rank of Group C*-algebras of Some Disconnected Lie Groups

  • Sudo, Takahiro
    • Kyungpook Mathematical Journal
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    • v.47 no.2
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    • pp.203-219
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    • 2007
  • We estimate the stable rank and connected stable rank of group $C^*$-algebra of certain disconnected solvable Lie groups such as semi-direct products of connected solvable Lie groups by the integers.

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STABLE RANK OF TWISTED CROSSED PRODUCTS OF $C^{*}-ALGEBRAS$ BY ABELIAN GROUPS

  • Sudo, Takahiro
    • The Pure and Applied Mathematics
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    • v.10 no.2
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    • pp.103-118
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    • 2003
  • We estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by topological Abelian groups. As an application we estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by solvable Lie groups. In particular, we obtain the stable rank estimate of twisted group $C^{*}-algebras$ of solvable Lie groups by the (reduced) dimension and (generalized) rank of groups.

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On the galois groups of the septic polynomials

  • Lee, Geon-No
    • Communications of the Korean Mathematical Society
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    • v.11 no.1
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    • pp.23-31
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    • 1996
  • Our main purpose in this paper is to determine the Galois group of the given irreducible septic polynomial ove Q by using three resolvant polynomials and the discriminant of the given polynomial.

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Equivalent classes of decouplable and controllable linear systems

  • Ha, In-Joong;Lee, Sung-Joon
    • 제어로봇시스템학회:학술대회논문집
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    • pp.405-412
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    • 1992
  • The problem we consider in this paper is more demanding than the problem of input-output linearization with state equivalence recently solved by Cheng, Isidori, Respondek, and Tarn. We request that the MIMO nonlinear system, for which the problem of input-output linearization with state-equivalence is solvable, can be decoupled. In exchange for further requirement like this, our problem produces more usable and informative results than the problem of input-output linearization with state-equivalence. We present the necessary and sufficient conditions for our problem to be solvable. We characterize each of the nonlinear systems satisfying these conditions by a set of parameters which are invariant under the group action of state feedback and transformation. Using this set of parameters, we can determine directly the unique one, among the canonical forms of decouplable and controllable linear systems, to which a nonlinear system can be transformed via appropriate state feedback and transformation. Finally, we present the necessary and sufficient conditions for our problem to be solvable with internal stability, that is, for stable decoupling.

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CYCLIC SUBGROUP SEPARABILITY OF HNN EXTENSIONS

  • Kim, Goansu
    • Bulletin of the Korean Mathematical Society
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    • v.30 no.2
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    • pp.285-293
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    • 1993
  • In [4], Baumslag and Tretkoff proved a residual finiteness criterion for HNN extensions (Theorem 1.2, below). This result has been used extensively in the study of the residual finiteness of HNN extensions. Note that every one-relator group can be embedded in a one-relator group whose relator has zero exponent sum on a generator, and the latter group can be considered as an HNN extension. Hence the properties of an HNN extension play an important role in the study of one-relator groups [3], [2]. In this paper we prove a criterion for HNN extensions to be .pi.$_{c}$(Theorem 2.2). Moreover, we can prove that certain one-relator groups, known to be residually finite, are actually .pi.$_{c}$. It was known by Mostowski [10] that the word problem is solvable for finitely presented, residually finite groups. In the same way, the power problem is solvable for finitely presented .pi.$_{c}$ groups. Another application of subgroup separability with respect to special subgroups was mentioned by Thurston [12, Problem 15].m 15].

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