A Class of Three-Generator, Three-Relation, Finite Groups
1970 ◽
Vol 22
(1)
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pp. 36-40
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Keyword(s):
Mennicke (2) has given a class of three-generator, three-relation finite groups. In this paper we present a further class of three-generator, threerelation groups which we show are finite.The groups presented are defined as:with α|γ| ≠ 1, β|γ| ≠ 1, γ ≠ 0.We prove the following result.THEOREM 1. Each of the groups presented is a finite soluble group.We state the following theorem proved by Macdonald (1).THEOREM 2. G1(α, β, 1) is a finite nilpotent group.1. In this section we make some elementary remarks.
1978 ◽
Vol 19
(2)
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pp. 153-154
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Keyword(s):
1990 ◽
Vol 33
(1)
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pp. 1-10
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Keyword(s):
1992 ◽
Vol 53
(3)
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pp. 352-368
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Keyword(s):
1974 ◽
Vol 17
(2)
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pp. 142-153
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Keyword(s):
2019 ◽
Vol 101
(2)
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pp. 247-254
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Keyword(s):
1975 ◽
Vol 27
(4)
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pp. 837-851
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1987 ◽
Vol 43
(2)
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pp. 220-223
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1992 ◽
Vol 162
(1)
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pp. 227-235