A Generalization of Final Rank of Primary Abelian
Groups
1970 ◽
Vol 22
(6)
◽
pp. 1118-1122
◽
Keyword(s):
Let G be a p-primary Abelian group. Recall that the final rank of G is infn∈ω{r(pnG)}, where r(pnG) is the rank of pnG and ω is the first limit ordinal. Alternately, if Γ is the set of all basic subgroups of G, we may define the final rank of G by supB∈Γ {r(G/B)}. In fact, it is known that there exists a basic subgroup B of G such that r(G/B) is equal to the final rank of G. Since the final rank of G is equal to the final rank of a high subgroup of G plus the rank of pωG, one could obtain the same information if the definition of final rank were restricted to the class of p-primary Abelian groups of length ω.
1981 ◽
Vol 33
(4)
◽
pp. 817-825
◽
Keyword(s):
1970 ◽
Vol 67
(1)
◽
pp. 1-11
◽
Keyword(s):
1995 ◽
Vol 44
(2)
◽
pp. 395-402
◽
Keyword(s):
2011 ◽
Vol 10
(03)
◽
pp. 377-389
Keyword(s):
2017 ◽
Vol 16
(10)
◽
pp. 1750200
◽
1981 ◽
Vol 90
(2)
◽
pp. 273-278
◽
Keyword(s):
2018 ◽
Vol 167
(02)
◽
pp. 229-247
Keyword(s):