BOUNDED GENERATION AND LINEAR GROUPS
2003 ◽
Vol 13
(04)
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pp. 401-413
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Keyword(s):
A group Γ is called boundedly generated (BG) if it is the set-theoretic product of finitely many cyclic subgroups. We show that a BG group has only abelian by finite images in positive characteristic representations.We use this to reprove and generalize Rapinchuk's theorem by showing that a BG group with the FAb property has only finitely many irreducible representations in any given dimension over any field. We also give a structure theorem for the profinite completion G of such a group Γ.On the other hand, we exhibit boundedly generated profinite FAb groups which do not satisfy this structure theorem.
Keyword(s):
2002 ◽
Vol 45
(2)
◽
pp. 180-195
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Keyword(s):
2005 ◽
Vol 04
(05)
◽
pp. 489-515
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1946 ◽
Vol 7
(4)
◽
pp. 196-203
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1999 ◽
Vol 173
◽
pp. 249-254
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1969 ◽
Vol 27
◽
pp. 6-7
Keyword(s):
1980 ◽
Vol 38
◽
pp. 30-33
2005 ◽
Vol 19
(3)
◽
pp. 129-132
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Keyword(s):