MAXIMAL SUBSETS OF PAIRWISE NONCOMMUTING ELEMENTS OF THREE-DIMENSIONAL GENERAL LINEAR GROUPS
2009 ◽
Vol 80
(1)
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pp. 91-104
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AbstractLet G be a group. A subset N of G is a set of pairwise noncommuting elements if xy⁄=yx for any two distinct elements x and y in N. If ∣N∣≥∣M∣ for any other set of pairwise noncommuting elements M in G, then N is said to be a maximal subset of pairwise noncommuting elements. In this paper we determine the cardinality of a maximal subset of pairwise noncommuting elements in a three-dimensional general linear group. Moreover, we show how to modify a given maximal subset of pairwise noncommuting elements into another maximal subset of pairwise noncommuting elements that contains a given ‘generating element’ from each maximal torus.
2005 ◽
Vol 92
(1)
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pp. 62-98
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1994 ◽
Vol 116
(1)
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pp. 7-25
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2011 ◽
Vol 83
(3)
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pp. 369-375
1990 ◽
Vol 107
(2)
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pp. 193-196
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2018 ◽
Vol 85
(3-4)
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pp. 422
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1969 ◽
Vol 21
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pp. 106-135
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1985 ◽
Vol 37
(2)
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pp. 238-259
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1978 ◽
Vol 78
(3-4)
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pp. 237-240
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