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On Hadamard Groups with Relatively Large 2-Subgroup

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2015

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
A Hadamard group is any group of order 4u2 that contain a difference set. In this paper we obtain some new conditions for Hadamard groups with relatively large 2-subgroup. We use norm invariant polynomials f (ǫ) ∈ Z[ǫ], | f (ǫt )| = const., where ǫ is root of unity of order 2n. Necessary condition on a size of normal cyclic 2-subgroup are given. Also, we have covered cases when 2-subgroup has generators similar to a modular or dihedral 2-group. Additionally, we construct such two infinite series of groups. Obtained results are natural generalization of a case when entire group is 2-group.
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REFERENCES

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