Groups with a given number of nonpower subgroups
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Date
Authors
Anabanti, Chimere S.
Hart, S.B.
Journal Title
Journal ISSN
Volume Title
Publisher
Cambridge University Press
Abstract
No group has exactly one or two nonpower subgroups. We classify groups containing exactly three nonpower subgroups and show that there is a unique finite group with exactly four nonpower subgroups. Finally, we show that given any integer k greater than 4 , there are infinitely many groups with exactly k nonpower subgroups.
Description
Keywords
Counting subgroups, Nonpower subgroups, Finite groups
Sustainable Development Goals
Citation
Anabanti, C.S. & Hart, S.B. 2022, 'Groups with a given number of nonpower subgroups', Bulletin of the Australian Mathematical Society, vol. 106, no. 2, pp. 315-319, doi : 10.1017/S0004972721001179.