n-Isoclinism Classes and n-Nilpotency Degree of Finite Groups
Gallagher (1970) and Gustafson (1973) introduced the commutativity degree of a finite group. In this paper, we define the n-nilpotency degree of finite groups for n ≥ 1, and prove some results as Lescot (1995) does for a certain class of groups. In particular, it is shown that the n-isoclinism of finite groups preserves their n-nilpotency degrees. Finally, some sharper and more general upper bound than previously known is constructed for the commutativity degree of non-abelian finite groups.
2006 ◽
Vol 74
(1)
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pp. 121-132
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1969 ◽
Vol 9
(3-4)
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pp. 467-477
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2017 ◽
Vol 16
(03)
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pp. 1750043
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1973 ◽
Vol 9
(2)
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pp. 267-274
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2016 ◽
Vol 15
(10)
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pp. 1650197
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1969 ◽
Vol 10
(3-4)
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pp. 359-362
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2021 ◽
Vol 58
(2)
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pp. 147-156
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