# Normal Determinability of Torsion-Free Abelian Groups by Their Holomorphs

## Abstract

We investigate torsion-free Abelian groups that are decomposable into direct sums or direct products of homogeneous groups normally defined by their holomorphs. Properties of normal Abelian subgroups of holomorphs of torsion-free Abelian groups are also studied.

- Authors:

- Tomsk State University (Russian Federation)
- Tomsk State University of Control Systems and Radioelectronics (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771357

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 3; Conference: 5. All-Russian symposium on abelian groups, Biysk (Russian Federation), 20-25 Aug 2012; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGEBRA; GROUP THEORY; TORSION

### Citation Formats

```
Grinshpon, S. Ya., E-mail: grinshpon@math.tsu.ru, and Grinshpon, I. E., E-mail: irina-grinshpon@yandex.ru.
```*Normal Determinability of Torsion-Free Abelian Groups by Their Holomorphs*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3743-Y.

```
Grinshpon, S. Ya., E-mail: grinshpon@math.tsu.ru, & Grinshpon, I. E., E-mail: irina-grinshpon@yandex.ru.
```*Normal Determinability of Torsion-Free Abelian Groups by Their Holomorphs*. United States. doi:10.1007/S10958-018-3743-Y.

```
Grinshpon, S. Ya., E-mail: grinshpon@math.tsu.ru, and Grinshpon, I. E., E-mail: irina-grinshpon@yandex.ru. Sun .
"Normal Determinability of Torsion-Free Abelian Groups by Their Holomorphs". United States. doi:10.1007/S10958-018-3743-Y.
```

```
@article{osti_22771357,
```

title = {Normal Determinability of Torsion-Free Abelian Groups by Their Holomorphs},

author = {Grinshpon, S. Ya., E-mail: grinshpon@math.tsu.ru and Grinshpon, I. E., E-mail: irina-grinshpon@yandex.ru},

abstractNote = {We investigate torsion-free Abelian groups that are decomposable into direct sums or direct products of homogeneous groups normally defined by their holomorphs. Properties of normal Abelian subgroups of holomorphs of torsion-free Abelian groups are also studied.},

doi = {10.1007/S10958-018-3743-Y},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 3,

volume = 230,

place = {United States},

year = {2018},

month = {4}

}

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