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RELATIVE RELATION MODULES OF FINITE ELEMENTARY ABELIAN p-GROUPS

Poonam Kumar Sharma|Mohammad Yamin
대한수학회 (The Korean Mathematical Society)|2014.08|대한수학회보 (Bulletin of the KMS)|제51권 제4호|pp. 1205-1210

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참고문헌

키워드

modulesfree groupsfree productsp-groupsrelation modules
주제분류수학

초록

Let E be a free product of a finite number of cyclic groups, and S a normal subgroup of E such that E/S = G is finite. For a prime p, ˆ S = S/S ′ Sp may be regarded as an FpG-module via conjugation in E. The aim of this article is to prove that ˆ S is decomposable into two indecomposable modules for finite elementary abelian p-groups G.

Abstract

Let E be a free product of a finite number of cyclic groups, and S a normal subgroup of E such that E/S = G is finite. For a prime p, ˆ S = S/S ′ Sp may be regarded as an FpG-module via conjugation in E. The aim of this article is to prove that ˆ S is decomposable into two indecomposable modules for finite elementary abelian p-groups G.

참고문헌 (9)

  1. W. Gaschutz, "Uber modulare Darstellungen endlicher Gruppen, die von freien Gruppen induziert warden", Math. Z, 60, pp.274~286 (1954)
  2. K. W. Gruenberg, "Relation modules of finite groups", Regional Conference Series in Math, (25) (1976), A.M.S. Providence
  3. W. Kimmerle, "Relative relation modules on generators for integral group rings of finite groups", Math. Z, 172, pp.143~156 (1980)
  4. L. G. Kovacs, "Lie powers of relation modules for groups", J. Algebra, 326(1), pp.192~200 (2011)
  5. J. N. Mittal, "Annihilators of relation modules", J. Austral. Math. Soc.(2), 16, pp.228~233 (1973)
  6. D. J. S. Robinson, "A Course in the Theory of Groups" (1996), Springer-Verlag
  7. P. K. Sharma, "Relative Relation Modules of SL(2, p) and PSL(2, p) groups", J. Indian Math Soc, 80(3-4), pp.341~348 (2013)
  8. M. Yamin, "Relative relation modules of finite groups", Proc. Edinburgh Math. Soc, 34(3), pp.433~442 (1991)
  9. M. Yamin, "Minimal relative relation modules of finite p-groups", Proc. Amer. Math. Soc, 118(1), pp.1~3 (1993)

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