What is it about?
Follwing results have been proved in this paper. 1. If a group has a solvable generating transversal with respect to a core-free subgroup, then the group is solvable. 2. Let S be a nilpotent right loop. Then the right inner mapping group RInn(S) is a solvable group.
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Why is it important?
Solvability of group in terms of generating transversal has not been defined before.
Perspectives
The concept of solvable right loop and nilpotent right loop is defined. Embedding of right loop as a transversal of a group and study solvability of the group is very interesting for me.
Vivek Jain
Central University of South Bihar
Read the Original
This page is a summary of: Solvable and nilpotent right loops, Acta Universitatis Sapientiae Mathematica, January 2017, De Gruyter,
DOI: 10.1515/ausm-2017-0013.
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