Lower bounds on conjugacy classes of non-nilpotent subgroups in a finite group
2014 ◽
Vol 14
(03)
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pp. 1550039
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Keyword(s):
For a finite group G, let γ(G) denote the number of conjugacy classes of all non-nilpotent subgroups of G, and let π(G) denote the set of the prime divisors of |G|. In this paper, we establish lower bounds on γ(G). In fact, we show that if G is a finite solvable group, then γ(G) = 0 or γ(G) ≥ 2|π(G)|-2, and if G is non-solvable, then γ(G) ≥ |π(G)| + 1. Both lower bounds are best possible.
2016 ◽
Vol 104
(1)
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pp. 37-43
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2020 ◽
Vol 30
(05)
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pp. 1073-1080
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2016 ◽
Vol 15
(03)
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pp. 1650057
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Keyword(s):
Keyword(s):
2010 ◽
Vol 17
(spec01)
◽
pp. 925-927
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2009 ◽
Vol 147
(3)
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pp. 567-577
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2011 ◽
Vol 54
(1)
◽
pp. 77-89
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2013 ◽
Vol 56
(3)
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pp. 873-886
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Keyword(s):
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