On locally finite groups whose derived subgroup is locally nilpotent
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DOI: 10.1002/mana.202400263
Abstract: A celebrated theorem of Helmut Wielandt shows that the nilpotent residual of the subgroup generated by two subnormal subgroups of a finite group is the subgroup generated by the nilpotent residuals of the subgroups. This… read more here.
Keywords: locally nilpotent; finite groups; derived subgroup; subgroup generated ... See more keywords
Recognizing the second derived subgroup of free groups
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DOI: 10.1016/j.jalgebra.2018.09.024
Abstract: Abstract The commutator subgroup of a free group is the subgroup consisting of elements contained in the kernel of every homomorphism from the free group to the integers. We give a similar characterization of the… read more here.
Keywords: free group; second derived; recognizing second; subgroup free ... See more keywords
The derived subgroup of linear and simply-connected o-minimal groups
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DOI: 10.1016/j.jalgebra.2019.02.022
Abstract: We show that the derived subgroup of a linear definable group in an o-minimal structure is also definable, extending the semialgebraic case proved by A. Pillay. We also show the definability of the derived subgroup… read more here.
Keywords: subgroup linear; connected minimal; linear simply; derived subgroup ... See more keywords