The combinatorics of normal subgroups in the unipotent upper triangular group

AbstractWe determine all the normal subgroups of the group of Cr diffeomorphisms of ℝn, 1≤r≤∞, except when r=n+1 or n=4, and also of the group of homeomorphisms of ℝn ( r=0). We also study the group A0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with non-empty boundary, then the quotient of A0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.

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Polygonal products of polycyclic by finite groups

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700021778 ◽

1996 ◽

Vol 54 (3) ◽

pp. 369-372 ◽

Cited By ~ 4

Author(s):

R.B.J.T. Allenby

Keyword(s):

Finite Groups ◽

Cyclic Subgroup ◽

Substantial Improvement ◽

Normal Subgroups ◽

Recent Theorem

We prove that a polygonal product of polycyclic by finite groups amalgamating normal subgroups, with trivial mutual intersections, is cyclic subgroup separable. Because of a recent example (stated below) of the author this substantial improvement on a recent theorem of Kim is essentially best possible.

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Bounds for the Number of Conjugacy Classes of Non-Normal Subgroups in a Finitep-Group

Communications in Algebra ◽

10.1080/00927870902828801 ◽

2009 ◽

Vol 37 (11) ◽

pp. 3928-3942

Author(s):

Gustavo A. Fernández-Alcober ◽

Leire Legarreta

Keyword(s):

Conjugacy Classes ◽

Normal Subgroups

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On CSQ-normal subgroups of finite groups

Open Mathematics ◽

10.1515/math-2016-0073 ◽

2016 ◽

Vol 14 (1) ◽

pp. 801-806

Author(s):

Yong Xu ◽

Xianhua Li

Keyword(s):

Finite Groups ◽

Normal Subgroups ◽

Sylow Subgroups

Abstract We introduce a new subgroup embedding property of finite groups called CSQ-normality of subgroups. Using this subgroup property, we determine the structure of finite groups with some CSQ-normal subgroups of Sylow subgroups. As an application of our results, some recent results are generalized.

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