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Addendum to ``On the Frattini subgroup''


Authors: John Cossey and Alice Whittemore
Journal: Proc. Amer. Math. Soc. 27 (1971), 63-64
MSC: Primary 20.54
DOI: https://doi.org/10.1090/S0002-9939-1971-0269744-0
Original Article: Proc. Amer. Math. Soc. 21 (1969), 699-702.
MathSciNet review: 0269744
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ F$ be a free group, $ R$ a normal subgroup of $ F$ and $ V$ a fully invariant subgroup of $ R$. In a recent paper the authors calculated the Frattini subgroup of $ F/V$ under suitable conditions on $ R$ and $ V$. This paper presents information on the Frattini subgroup of subgroups of $ F/V$ under the same conditions.


References [Enhancements On Off] (What's this?)

  • [1] G. Baumslag and K. W. Gruenberg, Some reflections on cohomological dimension and freeness, J. Algebra 6 (1967), 394-409. MR 38 #1150. MR 0232827 (38:1150)
  • [2] John Cossey and Alice Whittemore, On the Frattini subgroup, Proc. Amer. Math. Soc. 21 (1969), 699-702. MR 39 #2851. MR 0241511 (39:2851)
  • [3] Graham Higman, Finite groups having isomorphic images in every finite group of which they are homomorphic images, Quart. J. Math. Oxford Ser. (2) 6 (1955), 250-254. MR 19, 117. MR 0086061 (19:117d)
  • [4] V. G. Sokolov, The Frattini subgroup, Algebra i Logika 7 (1968), no. 2, 85-93. (Russian) MR 39 #1559. MR 0240207 (39:1559)
  • [5] John Stallings, On torsion-free groups with infinitely many ends, Ann. of Math. (2) 88 (1968), 312-334. MR 37 #4153. MR 0228573 (37:4153)
  • [6] R. Swan, (unpublished).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0269744-0
Keywords: Frattini subgroup, nilpotent variety of groups, solvable group
Article copyright: © Copyright 1971 American Mathematical Society

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