Groups with large conjugacy classes
1977 ◽
Vol 24
(3)
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pp. 257-265
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AbstractA finite group is called repetition-free if its conjugacy classes have distinct sizes. It is known that a supersolvable repetition-free group is necessarily isomorphie to Sym(3). the symmetric group on three symbols. Thus the question arises as to whether Sym (3) is the only repetition-free group. In this paper it is proved that if mk denotes the minimum of the orders of the centralizers of elements of a repetition-free group G and mk ≦ 4 then G is isomorphie to Sym (3).
1984 ◽
Vol 96
(2)
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pp. 195-201
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2008 ◽
Vol 40
(5)
◽
pp. 897-906
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1979 ◽
Vol 20
(1)
◽
pp. 57-70
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1982 ◽
Vol 33
(1)
◽
pp. 76-85
Keyword(s):
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2013 ◽
Vol 12
(05)
◽
pp. 1250204
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