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ISOMORPHIC MODULAR GROUP ALGEBRAS OF SEMI-COMPLETE PRIMARY ABELIAN GROUPS

  • DANCHEV, PETER V. (13 General Kutuzov Street)
  • Published : 2005.02.01
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Abstract

Suppose G is a semi-complete abelian p-group and FG ${\cong}$ FH as commutative unitary F-algebras of characteristic p for any fixed group H. Then, it is shown that, G ${\cong}$ H. This improves a result of the author proved in the Proceedings of the American Math. Society (2002) and also completely solves by an another method a long-standing problem of W. May posed in the same Proceedings (1979).

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References

  1. D. Beers, F. Richman, and E. Walker, Group algebras of abelian groups, Rend. Sem. Mat. Univ. Padova 69 (1983), 41-50
  2. P. V. Danchev, Commutative group algebras of cardinality $N_1$, Southeast Asian Bull. Math. 25 (2002), no. 4, 589-598 https://doi.org/10.1007/s100120200003
  3. P. V. Danchev, Commutative group algebras of direct sums of ${\sigma}-summable$ abelian p-groups, Math. J. Okayama Univ. 45 (2003), 1-15
  4. P. V. Danchev, Invariances in commutative and noncommutative group algebras, Compt. rend. Acad. bulg. Sci. 54 (2001), no. 4, 5-8
  5. P. V. Danchev, Isomorphism of commutative group algebras of closed p-groups and p-local algebraically compact groups, Proc. Amer. Math. Soc. 130 (2002), no. 7, 1937-1941
  6. P. V. Danchev, Isomorphism of commutative group algebras of mixed splitting groups, Compt. rend. Acad. bulg. Sci. 51 (1998), no. 1-2, 13-16
  7. P. V. Danchev, Isomorphism of modular group algebras of direct sums of torsion-complete abelian p-groups, Rend. Sem. Mat. Univ. Padova 101 (1999), 51-58
  8. P. V. Danchev, The splitting problem and the direct factor problem in modular abelian group algebras, Math. Balkanica (N.S.) 15 (2000), no. 3-4, 217-226
  9. P. V. Danchev, Units in abelian group rings of prime characteristic, Compt. rend. Acad. bulg. Sci. 48 (1995), no. 8, 5-8
  10. J. Irwin, F. Richman, and E. Walker, Countable direct sums of torsion complete groups, Proc. Amer. Math. Soc. 17 (1966), no. 4, 763-766
  11. G. Kolettis, Jr., Semi-complete primary abelian groups, Proc. Amer. Math. Soc. 11 (1960), no. 2, 200-205
  12. W. May, Modular group algebras of totally projective p-primary groups, Proc. Amer. Math. Soc. 76 (1979), no. 1, 31-34
  13. W. May, The direct factor problem for modular abelian group algebras, Contemp. Math. 93 (1989), 303-308 https://doi.org/10.1090/conm/093/1003359

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