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Short two-variable identities for finite groups

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Published/Copyright: September 19, 2008
Journal of Group Theory
From the journal Volume 11 Issue 5

Abstract

In this paper, we consider finite groups G satisfying identities of the form

.

We focus on identities with r small, , and all coprime to the order of G. We show that for r = 2,3 and 5, G must be nilpotent. We also classify for r = 4,6 and 7, the special identities which can hold in non-nilpotent groups. Finally, we show that for r < 30, the group G must be solvable.

Received: 2007-04-09
Revised: 2007-10-18
Published Online: 2008-09-19
Published in Print: 2008-September

© de Gruyter 2008

Articles in the same Issue

  1. Generation gaps and abelianized defects of free products
  2. Abelian-by-polycyclic groups of homological type FP3
  3. Conjugacy in lattice-ordered groups and right ordered groups
  4. An approach to duality on abelian precompact groups
  5. Special abelian Moufang sets of finite Morley rank
  6. Cross characteristic representations of 3D4(q) are reducible over proper subgroups
  7. Examples of 3-dimensional 1-cohomology for absolutely irreducible modules of finite simple groups
  8. Short two-variable identities for finite groups
  9. Schur indices and commutators in supersolvable groups
  10. Two dual questions on zeros of characters of finite groups
  11. Supercharacters of the adjoint group of a finite radical ring
https://doi.org/10.1515/JGT.2008.043

Articles in the same Issue

  1. Generation gaps and abelianized defects of free products
  2. Abelian-by-polycyclic groups of homological type FP3
  3. Conjugacy in lattice-ordered groups and right ordered groups
  4. An approach to duality on abelian precompact groups
  5. Special abelian Moufang sets of finite Morley rank
  6. Cross characteristic representations of 3D4(q) are reducible over proper subgroups
  7. Examples of 3-dimensional 1-cohomology for absolutely irreducible modules of finite simple groups
  8. Short two-variable identities for finite groups
  9. Schur indices and commutators in supersolvable groups
  10. Two dual questions on zeros of characters of finite groups
  11. Supercharacters of the adjoint group of a finite radical ring
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