47:) and by László Fuchs (in general) in an attempt to formulate classification theory of infinite abelian groups that goes beyond the
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and satisfies further technical conditions. This notion was introduced by L. Ya. Kulikov (for
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between two well understood classes of abelian groups: direct sums of cyclic groups and
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293:; i.e., have bounded exponent. In general, the isomorphism class of the quotient,
51:. It helps to reduce the classification problem to classification of possible
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328:. Pure and Applied Mathematics, Vol. 36. New York–London: Academic Press
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25:
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278:-basic subgroup have been completely characterized. For the case of
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On the theory of abelian groups of arbitrary cardinality
216:. Picking a generator in each cyclic direct summand of
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are isomorphic. Abelian groups that contain a unique
190:, which moreover coincides with the topology
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341:(in Russian), Mat. Sb., 16 (1945), 129–162
170:Conditions 1–3 imply that the subgroup,
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104:, if the following conditions hold:
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326:Infinite abelian groups, Vol. I
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123:and infinite cyclic groups;
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258:-basic subgroups for each
233:, which is analogous to a
63:Definition and properties
379:Infinite group theory
352:, New York: Chelsea,
324:László Fuchs (1970),
303:by a basic subgroup,
248:Every abelian group,
374:Abelian group theory
350:The theory of groups
268:-basic subgroups of
148:The quotient group,
384:Subgroup properties
113:is a direct sum of
243:free abelian group
184:-adic topology of
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337:L. Ya. Kulikov,
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309:, may depend on
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285:they are either
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18:abstract algebra
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96:prime number
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254:, contains
200:, and that
32:which is a
368:Categories
319:References
222:creates a
53:extensions
34:direct sum
287:divisible
178:Hausdorff
117:of order
348:(1960),
77:, of an
69:subgroup
26:subgroup
358:0109842
333:0255673
291:bounded
283:-groups
192:induced
180:in the
158:, is a
45:-groups
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227:-basis
92:-basic
28:of an
241:or a
237:of a
235:basis
208:dense
194:from
176:, is
131:is a
24:is a
20:, a
289:or
229:of
210:in
206:is
139:of
36:of
16:In
370::
354:MR
330:MR
315:.
245:.
98:,
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67:A
59:.
312:B
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298:/
296:A
281:p
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166:.
162:-
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153:/
151:A
145:;
142:A
135:-
133:p
128:B
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110:B
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90:p
84:A
74:B
43:p
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