Transversals in Groups
نویسندگان
چکیده
منابع مشابه
Transversals in non-discrete groups
The concept of ‘topological right transversal’ is introduced to study right transversals in topological groups. Given any right quasigroup S with a Tychonoff topology T , it is proved that there exists a Hausdorff topological group in which S can be embedded algebraically and topologically as a right transversal of a subgroup (not necessarily closed). It is also proved that if a topological rig...
متن کاملConnected transversals to nilpotent groups
We prove that a finite group with nilpotent subgroup H and H-connected transversals is solvable. The proof depends on the classification of finite simple groups.
متن کاملA study of Nilpotent groups through right transversals
In group theory nilpotency of a group has a great importance. In this paper we have studied some concept of nilpotency through right transversals. We have also studied prime power groups and frattini subgroups through right transversals.
متن کاملTransversals in Trees
The n− 2 upper bounds in (1) are attained simultaneously if and only if T is the path (the tree with precisely one leaf); the n− 2 lower bounds in (1) are attained simultaneously if and only if T is the star (the tree where all leaves are children of the root). Jonathan David Farley asked how high can these lower bounds be raised if each node of T has at most two children; he offered a creative...
متن کاملCommon Transversals
Given t families, each family consisting of s finite sets, we show that if the families “separate points" in a natural way, and if the union of all the sets in all the families contains more than (s+1)t st 1 1 elements, then a common transversal of the t families exists. In case each family is a covering family, the bound is st st 1. Both of these bounds are best possible. This work extends rec...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1996
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0109