Results 101 to 110 of about 1,123 (133)
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The supersolvable residual of an -group
Mathematical Proceedings of the Cambridge Philosophical Society, 1976Let be the class of groups possessing a subgroup of index n for each divisor n of the group order. McLain (7) initiated the formal investigation of and observed that every solvable group is a direct factor of an -group. However, subclasses of provide some interesting problems.
Ben Brewster, Malcolm Ottaway
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Communications in Mathematics and Statistics, 2015
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Guo, Wenbin, Kondrat'ev, A. S.
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Guo, Wenbin, Kondrat'ev, A. S.
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Schur indices and commutators in supersolvable groups
Journal of Group Theory, 2008\textit{U. Riese} and \textit{P. Schmid}, [in J. Algebra 182, No. 1, 183-200 (1996; Zbl 0859.20006)], proved that if the finite group \(G\) is supersolvable, then \(m(\chi)\) divides \(|G/G'|\) for all irreducible characters \(\chi\) of \(G\), where \(m(\chi)\) denotes the Schur index of \(\chi\) over the rational numbers.
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A Frobenius-type theorem for supersolvable groups
Publicationes Mathematicae Debrecen, 1996Let \(p\) be a prime. A group \(G\) is said to be strictly \(p\)-closed whenever \(G_p\), a Sylow \(p\)-subgroup of \(G\) is normal in \(G\) with \(G/G_p\) Abelian of exponent dividing \(p-1\). The main results of this paper are the following theorems: Theorem 1. Let \(G\) be a \(p\)-solvable group and \(N\) a normal subgroup of \(G\) such that \(G/N\)
Wang, Caiyun, Guo, Xiuyun
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Artinian rings with supersolvable adjoint group
Archiv der Mathematik, 2008The set of all elements of an associative ring R, not necessarily with a unit element, forms a monoid under the circle operation a ° b = a + b + ab. The group of all invertible elements of this monoid is called the adjoint group of R and is denoted by R°. It is proved that an artinian ring R with supersolvable adjoint group R° must be Lie supersolvable.
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Frattini subgroups ofp-closed andp-supersolvable groups
Israel Journal of Mathematics, 1974A nonabelianp-group with cyclic center cannot occur as a normal subgroup contained in the Frattini subgroup of ap-closed group. If a nonabelian normal subgroup of orderpn and nilpotence classk is contained in the Frattini subgroup of ap-closed group, then its exponent is a divisor ofpn−k.
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Cancer statistics for adolescents and young adults, 2020
Ca-A Cancer Journal for Clinicians, 2020Kimberly D Miller +2 more
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