The skeleton of a variety of groups
1972 ◽
Vol 6
(3)
◽
pp. 357-378
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Keyword(s):
The skeleton of a variety of groups is defined to be the intersection of the section closed classes of groups which generate . If m is an integer, m > 1, is the variety of all abelian groups of exponent dividing m, and , is any locally finite variety, it is shown that the skeleton of the product variety is the section closure of the class of finite monolithic groups in . In particular, S) generates . The elements of S are described more explicitly and as a consequence it is shown that S consists of all finite groups in if and only if m is a power of some prime p and the centre of the countably infinite relatively free group of , is a p–group.
2010 ◽
Vol 20
(05)
◽
pp. 671-688
Keyword(s):
1993 ◽
Vol 114
(1)
◽
pp. 143-147
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Keyword(s):
1989 ◽
Vol 46
(2)
◽
pp. 177-183
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Keyword(s):
1999 ◽
Vol 67
(3)
◽
pp. 329-355
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1987 ◽
Vol 30
(1)
◽
pp. 115-120
Keyword(s):
1998 ◽
Vol 08
(04)
◽
pp. 443-466
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1974 ◽
Vol 17
(2)
◽
pp. 222-233
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Keyword(s):
Keyword(s):