Solvable Groups and Loops
β Scribed by Ari Vesanen
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 168 KB
- Volume
- 180
- Category
- Article
- ISSN
- 0021-8693
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π SIMILAR VOLUMES
Let L be an RA loop, that is, a loop whose loop ring in any characteristic is an alternative, but not associative, ring. We find necessary and sufficient conditions Ε½ . for the Moufang unit loop of RL to be solvable when R is the ring of rational integers or an arbitrary field.
A G-loop is a loop which is isomorphic to all its loop isotopes. We apply some theorems about permutation groups to get information about G-loops. In particular, we study G-loops of order pq, where p < q are primes and p q -1 . In the case p = 3, the only G-loop of order 3q is the group of order 3q.
For any connected Lie group G, we introduce the notion of exponential radical Exp G that is the set of all strictly exponentially distorted elements of G. In case G is a connected simply-connected solvable Lie group, we prove that Exp G is a connected normal Lie subgroup in G and the exponential rad
We determine the positive integers n for which there exist a solvable group G and two non-conjugate subgroups of index n in G that induce the same permutation character.