Abstract
Assume G is a direct product of M p (1, 1, 1) and an elementary abelian p-group, where M p (1, 1, 1) = 〈a, b | a p = b p = c p =1, [a,b]=c,[c,a] = [c,b]=1〉. When p is odd, we prove that G is the group whose number of subgroups is maximal except for elementary abelian p-groups. Moreover, the counting formula for the groups is given.
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This work was supported by NSFC (No. 11071150), by NSF of Shanxi Province (No. 2012011001-3) and Shanxi Scholarship Council of China ([2011]8-059).
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Qu, H. Finite non-elementary abelian p-groups whose number of subgroups is maximal. Isr. J. Math. 195, 773–781 (2013). https://doi.org/10.1007/s11856-012-0114-0
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DOI: https://doi.org/10.1007/s11856-012-0114-0