A Note on Special Local 2-Nilpotent Groups and the Solvability of Finite Groups
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A finite group G is called a special local 2-nilpotent group if G is not 2-nilpotent, the Sylow 2-subgroup P of G has a section isomorphic to the quaternion group of order 8, [Formula: see text] and NG(P) is 2-nilpotent. In this paper, it is shown that SL2(q), [Formula: see text], is a special local 2-nilpotent group if and only if [Formula: see text], and that GL2(q), [Formula: see text], is a special local 2-nilpotent group if and only if q is odd. Moreover, the solvability of finite groups is also investigated by giving two generalizations of a result from [A note on p-nilpotence and solvability of finite groups, J. Algebra 321 (2009) 1555–1560].
2017 ◽
Vol 16
(02)
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pp. 1750025
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1956 ◽
Vol 52
(1)
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pp. 5-11
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2019 ◽
Vol 19
(12)
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pp. 2150001
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2013 ◽
Vol 13
(02)
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pp. 1350100
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1985 ◽
Vol 32
(2)
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pp. 293-297
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