Groups whose Chermak–Delgado lattice is a subgroup lattice of an elementary abelian <i>p</i>-group

نویسندگان

چکیده

The Chermak–Delgado lattice of a finite group G is self-dual sublattice the subgroup G. In this paper, we focus on groups whose an elementary abelian p-group. We prove that such are nilpotent class 2. also that, for any p-group E, there exists E.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Subgroup Lattice of an Abelian Finite Group

The aim of this paper is to give some connections between the structure of an abelian finite group and the structure of its subgroup lattice. Let (G, +) be an abelian group. Then the set L(G) of subgroups of G is a modular and complete lattice. Moreover, we suppose that G is finite of order n. If L n is the divisors lattice of n, then the following function is well defined: ord : L(G) −→ L n , ...

متن کامل

On the Congruence Lattice of an Abelian Lattice Ordered Group

In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.

متن کامل

Free abelian lattice-ordered groups

Let n be a positive integer and FA`(n) be the free abelian latticeordered group on n generators. We prove that FA`(m) and FA`(n) do not satisfy the same first-order sentences in the language L={+,−, 0,∧,∨} if m 6= n. We also show that Th(FA`(n)) is decidable iff n ∈ {1, 2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices. A. M. S. C...

متن کامل

Lattice of compactifications of a topological group

We show that the lattice of compactifications of a topological group $G$ is a complete lattice which is isomorphic to the lattice of all closed normal subgroups of the Bohr compactification $bG$ of $G$. The correspondence defines a contravariant functor from the category of topological groups to the category of complete lattices. Some properties of the compactification lattice of a topological ...

متن کامل

Spectra of Abelian Weakly Associative Lattice Groups

The notion of a weakly associative lattice group is a generalization of that of a lattice ordered group in which the identities of associativity of the lattice operations join and meet are replaced by the identities of weak associativity. In the paper, the spectral topologies on the sets of straightening ideals (and on some of their subsets) of abelian weakly associative lattice groups are intr...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Communications in Algebra

سال: 2021

ISSN: ['1532-4125', '0092-7872']

DOI: https://doi.org/10.1080/00927872.2021.2021222