Finite rings with homocyclic $p-$groups as Sylow $p$-subgroups of the group of units

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dc.contributor.authorChikunji, Chiteng'A John
dc.date.accessioned2021-05-12T10:01:53Z
dc.date.available2021-05-12T10:01:53Z
dc.date.issued2017
dc.descriptionPaper presented at the 4th Strathmore International Mathematics Conference (SIMC 2017), 19 - 23 June 2017, Strathmore University, Nairobi, Kenya.en_US
dc.description.abstractIn 1960, Laszlo Fuchs posed, among other problems, the following: characterize the groups which are the groups of all units in a commutative and associative ring with identity. Though this problem still remains open, attempts have been made to solve it for various classes of groups, where the rings are not assumed to be commutative. In this paper, we focus on a slightly weaker version of Fuchs' problem by determining completely primary finite rings whose unit groups have homocyclic Sylow $p$-subgroups with prime power exponents. We further investigate the constraints on the rings with no homocyclic Sylow $p-$subgroups of the unit groups.en_US
dc.identifier.urihttp://hdl.handle.net/11071/11838
dc.language.isoenen_US
dc.publisherStrathmore Universityen_US
dc.subjectFinite ringsen_US
dc.subjectHomocyclic $p-$groupsen_US
dc.subjectSylow $p$-subgroupsen_US
dc.titleFinite rings with homocyclic $p-$groups as Sylow $p$-subgroups of the group of unitsen_US
dc.typeArticleen_US
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