On the finite $p$-groups with unique cyclic subgroup of given order | Zendy

Libo Zhao | Zendy; Yangming LI | Zendy; u L" GONG | Zendy

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On the finite $p$-groups with unique cyclic subgroup of given order

Author(s) -

Libo Zhao,

Yangming LI,

u L" GONG

Publication year - 2016

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1501-70

Subject(s) - mathematics , order (exchange) , characteristic subgroup , maximal subgroup , index of a subgroup , cyclic group , combinatorics , subgroup , commutator subgroup , torsion subgroup , p group , abelian group , omega and agemo subgroup , class (philosophy) , group (periodic table) , finite group , pure mathematics , normal subgroup , elementary abelian group , physics , computer science , finance , quantum mechanics , artificial intelligence , economics

In this paper, we prove that if G is nonabelian and |G| > p , then G has a unique cyclic subgroup of order p with m ≥ 3 if and only if G has a unique abelian subgroup of order p if and only if G is a 2-group of maximal class.

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