| Title:
|
Commutative group algebras of highly torsion-complete abelian $p$-groups (English) |
| Author:
|
Danchev, Peter |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
587-592 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A new class of abelian $p$-groups with all high subgroups isomorphic is defined. Commutative modular and semisimple group algebras over such groups are examined. The results obtained continue our recent statements published in Comment. Math. Univ. Carolinae (2002). (English) |
| Keyword:
|
high subgroups |
| Keyword:
|
torsion-complete groups |
| Keyword:
|
group algebras |
| Keyword:
|
direct factors |
| MSC:
|
16S34 |
| MSC:
|
16U60 |
| MSC:
|
20C07 |
| MSC:
|
20K10 |
| MSC:
|
20K27 |
| idZBL:
|
Zbl 1101.20001 |
| idMR:
|
MR2062875 |
| . |
| Date available:
|
2009-01-08T19:31:24Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119413 |
| . |
| Reference:
|
[1] Culter D.O.: Primary abelian groups having all high subgroups isomorphic.Proc. Amer. Math. Soc. (3) 83 (1981), 467-470. MR 0627671 |
| Reference:
|
[2] Culter D.O.: High subgroups of primary abelian groups of length $ømega+n$.J. Algebra 83 (1983), 502-509. MR 0714261 |
| Reference:
|
[3] Danchev P.V.: Normed unit groups and direct factor problem for commutative modular group algebras.Math. Balkanica (2-3) 10 (1996), 161-173. Zbl 0980.16500, MR 1606535 |
| Reference:
|
[4] Danchev P.V.: Isomorphism of commutative semisimple group algebras.Math. Balkanica (1-2) 11 (1997), 51-55. Zbl 0939.16015, MR 1606596 |
| Reference:
|
[5] Danchev P.V.: Isomorphism of modular group algebras of direct sums of torsion-complete abelian $p$-groups.Rend. Sem. Mat. Univ. Padova 101 (1999), 51-58. Zbl 0959.20003, MR 1705279 |
| Reference:
|
[6] Danchev P.V.: Commutative group algebras of cardinality $\aleph_1$.Southeast Asian Bull. Math. (4) 25 (2001), 589-598. MR 1934659 |
| Reference:
|
[7] Danchev P.V.: Commutative modular group algebras of $p$-mixed and $p$-splitting abelian $\Sigma$-groups.Comment. Math. Univ. Carolinae 43 (2002), 419-428. Zbl 1068.16042, MR 1920518 |
| Reference:
|
[8] Danchev P.V.: Invariants for group algebras of abelian groups.Rend. Circolo Mat. Palermo (2) 51 (2002), 391-402. Zbl 1097.20504, MR 1947462 |
| Reference:
|
[9] Danchev P.V.: Isomorphism of commutative group algebras of closed $p$-groups and $p$-local algebraically compact groups.Proc. Amer. Math. Soc. 130 (2002), 1937-1941. Zbl 0997.20007, MR 1896025 |
| Reference:
|
[10] Danchev P.V.: Sylow $p$-subgroups of abelian group rings.Serdica Math. J. 29 (2003), 33-44. Zbl 1035.16025, MR 1981103 |
| Reference:
|
[11] Danchev P.V.: Isomorphic commutative group algebras of primary semi-complete abelian groups.to appear. |
| Reference:
|
[12] Danchev P.V.: Torsion completeness of Sylow $p$-groups in semi-simple group rings.Acta Math. Sinica (2003). |
| Reference:
|
[13] Danchev P.V.: Commutative group algebras of $p^{ømega+n}$-projective abelian groups.submitted. Zbl 1111.20007 |
| Reference:
|
[14] Danchev P.V.: $S(RG)/G_p$ is a $\Sigma$-group.in press. |
| Reference:
|
[15] Fuchs L.: Infinite Abelian Groups.I and II, Mir, Moscow, 1974 and 1977 (in Russian). Zbl 0338.20063, MR 0457533 |
| Reference:
|
[16] Hill P.D.: The equivalence of high subgroups.Proc. Amer. Math. Soc. 88 (1983), 207-211. Zbl 0522.20038, MR 0695242 |
| Reference:
|
[17] Irwin J.M.: High subgroups of abelian torsion groups.Pacific J. Math. 11 (1961), 1375-1384. Zbl 0106.02303, MR 0136654 |
| Reference:
|
[18] Irwin J.M., Cellars R.M., Snabb T.: A functorial generalization of Ulm's theorem.Comment. Math. Univ. St. Pauli 27 (1978), 155-177. MR 0546205 |
| Reference:
|
[19] Irwin J.M., Richman F., Walker E.A.: Countable direct sums of torsion complete groups.Proc. Amer. Math. Soc. 17 (1966), 763-766. Zbl 0143.04501, MR 0197556 |
| Reference:
|
[20] Irwin J.M., Snabb T., Cellars R.M.: The torsion product of totally projective $p$-groups.Comment. Math. Univ. St. Pauli 29 (1980), 1-5. Zbl 0441.20035, MR 0586242 |
| Reference:
|
[21] Mollov T.Zh.: Sylow $p$-subgroups of the group of normed units of semisimple group algebras of uncountable abelian $p$-groups.Pliska Stud. Math. Bulgar. 8 (1986), 34-46 (in Russian). MR 0866643 |
| . |
