A Menon-type identity with many tuples of group of units in residually finite Dedekind domains
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DOI: 10.1016/j.jnt.2016.11.023
Abstract: Abstract B. Sury proved the following Menon-type identity, ∑ a ∈ U ( Z n ) , b 1 , ⋯ , b r ∈ Z n gcd ( a − 1 , b… read more here.
Keywords: group units; menon type; type identity; identity ... See more keywords
Fuchs' problem for p-groups
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DOI: 10.1016/j.jpaa.2019.02.008
Abstract: Abstract Which groups can be the group of units in a ring? This open question, posed by Laszlo Fuchs in 1960, has been studied by the authors and others with a variety of restrictions on… read more here.
Keywords: group units; fuchs problem; class; group ... See more keywords
Normal subgroups of the group of units of incidence algebras
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DOI: 10.1016/j.laa.2019.10.017
Abstract: Abstract We investigate the group of units of incidence algebras and its normal subgroups. This includes a detailed discussion of the structure and properties of maximal abelian, normal subgroups, and criteria for solvability and nilpotency. read more here.
Keywords: group units; normal subgroups; units incidence; incidence algebras ... See more keywords
On group algebras whose group of units has maximal derived length
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DOI: 10.1080/00927872.2018.1499925
Abstract: Abstract Let G be a finite p-group, and let F be a field of characteristic p. C. Bagiński proved that if is cyclic of order pn, then the derived length of the group of units… read more here.
Keywords: group units; whose group; units maximal; group algebras ... See more keywords