Ulm-Kaplansky invariants of S(KG)/G

• Autorzy: Danchev P. V.

Identyfikatory

DOI

10.4064/ba53-2-4

• Języki publikacji: EN

Abstrakty

EN

Let G be an infinite abelian p-group and let K be a field of the first kind with respect to p of characteristic different from p such that s_p(K) = N or s_p (K) = N∪{0}. The main result of the paper is the computation of the Ulm–Kaplansky functions of the factor group S(KG)/G of the normalized Sylow p-subgroup S(KG) in the group ring KG modulo G. We also characterize the basic subgroups of S(KG)/G by proving that they are isomorphic to S(KB)/B, where B is a basic subgroup of G.

Słowa kluczowe

EN

Ulm-Kaplansky invariants; group rings

PL

niezmiennik Ulma-Kaplansky'ego; grupy pierścieni

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 2
• Strony: 147--156
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Danchev P. V.

• 13, General Kutuzov Street, block 7, floor 2, flat 4, 4003 Plovdiv, Bulgaria

Bibliografia

• [D0] P. Danchev, Sylow p-subgroups of commutative group algebras, C. R. Acad. Bulg. Sci. 46 (1993), no. 5, 13–14.
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• [D2] —, Commutative group algebras of abelian Σ-groups, Math. J. Okayama Univ. 40 (1998), 77–90.
• [D3] P. Danchev, Sylow p-subgroups of commutative modular and semisimple group rings, C. R. Acad. Bulg. Sci. 54 (2001), no. 6, 5–6.
• [D4] —, Basic subgroups in abelian group rings, Czechoslovak Math. J. 52 (2002), 129–140.
• [D5] —, Sylow p-subgroups of abelian group rings, Serdica Math. J. 29 (2003), 33–44.
• [D6] —, Ulm–Kaplansky invariants for S(RG)/Gp, Bull. Inst. Math. Acad. Sinica (2) 32 (2004), 133–144.
• [D7] —, Torsion completeness of Sylow p-groups in semisimple group rings, Acta Math. Sinica 20 (2004), 893–898.
• [D8] —, Commutative group algebras of summable abelian p-groups, Comm. Algebra, in press.
• [F] L. Fuchs, Infinite Abelian Groups, I and II, Mir, Moscow, 1974 and 1977 (in Russian).
• [K] G. Karpilovsky, Unit Groups of Group Rings, North-Holland, Amsterdam, 1989.
• [May] W. May, Modular group algebras of totally projective p-primary groups, Proc. Amer. Math. Soc. 76 (1979), 31–34.
• [M1] T. Zh. Mollov, 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).
• [M2] —, Unit groups of semisimple group algebras, ibid., 54–64 (in Russian).
• [M3] —, Ulm–Kaplansky invariants of Sylow p-subgroups of the group of normed units of semisimple group algebras of infinite separable abelian p-groups, ibid., 101–106 (in Russian).