The Number of Subgroup Chains of Finite Nilpotent Groups
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In this paper, we mainly count the number of subgroup chains of a finite nilpotent group. We derive a recursive formula that reduces the counting problem to that of finite p-groups. As applications of our main result, the classification problem of distinct fuzzy subgroups of finite abelian groups is reduced to that of finite abelian p-groups. In particular, an explicit recursive formula for the number of distinct fuzzy subgroups of a finite abelian group whose Sylow subgroups are cyclic groups or elementary abelian groups is given.
2005 ◽
Vol 71
(3)
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pp. 487-492
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1960 ◽
Vol 12
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pp. 447-462
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2011 ◽
Vol 12
(01n02)
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pp. 125-135
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2019 ◽
Vol 150
(4)
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pp. 1937-1964
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2015 ◽
Vol 92
(1)
◽
pp. 24-31
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2002 ◽
Vol 72
(2)
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pp. 173-180
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