JP Journal of Algebra, Number Theory and Applications
Volume 44, Issue 2, Pages 251 - 260
(November 2019) http://dx.doi.org/10.17654/NT044020251 |
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ON A SPECIAL CLASS OF FINITE p-GROUPS OF MAXIMAL CLASS AND EXPONENT p
M. E. Charkani and N. Snanou
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Abstract: Let p be a prime number and G be a finite nonabelian p-group. The group G is called a CGZ-group if and only if every nonabelian subgroup H of G satisfies CG(H) = Z(H). In this paper, we study the isomorphism classes of CGZ-groups of exponent p. More precisely, we prove that any CGZ-group G of order pn and exponent p (where 3 ≤ n ≤ p) admits a unique characteristic elementary abelian subgroup of index p. Furthermore, we study the isomorphism classes of splits extensions of an abelian group by a cyclic group. As an application, we compute the number of isomorphism classes of CGZ-groups of order pn and exponent p. |
Keywords and phrases: CGZ-group, p-group of maximal class, isomorphism classes, elementary abelian subgroup.
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