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A study of enhanced power graphs of finite groups
Journal of Algebra and its Applications, 2020The enhanced power graph [Formula: see text] of a group [Formula: see text] is the graph with vertex set [Formula: see text] such that two vertices [Formula: see text] and [Formula: see text] are adjacent if they are contained in the same cyclic subgroup.
Samir Zahirović +2 more
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The Character Theory of Finite Groups of Lie Type
, 2020Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics.
M. Geck, G. Malle
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Journal of the London Mathematical Society, 2000
A group is called homogeneous if any isomorphism between two finitely generated subgroups is induced by some automorphism. In [J. Lond. Math. Soc., II. Ser. 44, No. 1, 102-120 (1991; Zbl 0789.20033)] the authors classified homogeneous finite solvable groups.
Cherlin, Gregory, Felgner, Ulrich
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A group is called homogeneous if any isomorphism between two finitely generated subgroups is induced by some automorphism. In [J. Lond. Math. Soc., II. Ser. 44, No. 1, 102-120 (1991; Zbl 0789.20033)] the authors classified homogeneous finite solvable groups.
Cherlin, Gregory, Felgner, Ulrich
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Finite Permutation Groups and Finite Simple Groups
Bulletin of the London Mathematical Society, 1981In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced.
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Siberian Mathematical Journal, 2007
Summary: We study the so-called finite tangled groups. These are the groups in which every subset containing 1 and closed under the operation \(x\circ y=xy^{-1}x\) is a subgroup. The general problem of studying such groups reduces to the case of tangled groups of odd order. We classify all finite nilpotent tangled groups.
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Summary: We study the so-called finite tangled groups. These are the groups in which every subset containing 1 and closed under the operation \(x\circ y=xy^{-1}x\) is a subgroup. The general problem of studying such groups reduces to the case of tangled groups of odd order. We classify all finite nilpotent tangled groups.
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Journal of Soviet Mathematics, 1989
The present survey has been composed mainly on the basis of works reviewed in the R. Zh. Mat. over the years 1976-1983 and is a continuation of the surveys published in the years 1966, 1971, 1976 in this series. The main attention is paid to finite simple groups and their classification. The bibliography contains 1566 references.
Kondrat'ev, A. S. +2 more
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The present survey has been composed mainly on the basis of works reviewed in the R. Zh. Mat. over the years 1976-1983 and is a continuation of the surveys published in the years 1966, 1971, 1976 in this series. The main attention is paid to finite simple groups and their classification. The bibliography contains 1566 references.
Kondrat'ev, A. S. +2 more
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Journal of Mathematical Sciences, 1998
The present survey is based mainly on papers presented over the years 1983-1992 and can be considered as a continuation of the corresponding sections of the surveys ``Finite groups'' published in the years 1966, 1971, 1976 and 1986 by different authors (1966; Zbl 0207.33302, 1971; Zbl 0224.20006, 1976; Zbl 0444.20011, 1986; Zbl 0632.20009).
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The present survey is based mainly on papers presented over the years 1983-1992 and can be considered as a continuation of the corresponding sections of the surveys ``Finite groups'' published in the years 1966, 1971, 1976 and 1986 by different authors (1966; Zbl 0207.33302, 1971; Zbl 0224.20006, 1976; Zbl 0444.20011, 1986; Zbl 0632.20009).
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Nonsoluble and non-p-soluble length of finite groups
, 2013Every finite group G has a normal series each of whose factors either is soluble or is a direct product of nonabelian simple groups. We define the nonsoluble length λ(G) as the number of nonsoluble factors in a shortest series of this kind.
E. Khukhro, P. Shumyatsky
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