| Title:
|
A note on a class of factorized $p$-groups (English) |
| Author:
|
Jabara, Enrico |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
993-996 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we study finite $p$-groups $G=AB$ admitting a factorization by an Abelian subgroup $A$ and a subgroup $B$. As a consequence of our results we prove that if $B$ contains an Abelian subgroup of index $p^{n-1}$ then $G$ has derived length at most $2n$. (English) |
| Keyword:
|
factorizable groups |
| Keyword:
|
products of subgroups |
| Keyword:
|
$p$-groups |
| MSC:
|
20D15 |
| MSC:
|
20D40 |
| idZBL:
|
Zbl 1081.20034 |
| idMR:
|
MR2184379 |
| . |
| Date available:
|
2009-09-24T11:29:41Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128040 |
| . |
| Reference:
|
[1] B. Amberg, S. Franciosi and F. de Giovanni: Products of Groups.Clarendon Press, Oxford, 1992. MR 1211633 |
| Reference:
|
[2] J. Cossey and S. Stonehewer: On the derived length of finite dinilpotent groups.Bull. London Math. Soc. 30 (1998), 247–250. MR 1608098, 10.1112/S0024609397004050 |
| Reference:
|
[3] A. Mann: The derived length of $p$-groups.J. Algebra 224 (2000), 263–267. Zbl 0953.20008, MR 1739580, 10.1006/jabr.1998.8045 |
| Reference:
|
[4] M. Morigi: A note on factorized (finite) groups.Rend. Sem. Mat. Padova 98 (1997), 101–105. MR 1492971 |
| Reference:
|
[5] E. A. Pennington: On products of finite nilpotent groups.Math. Z. 134 (1973), 81–83. MR 0325764, 10.1007/BF01219093 |
| . |
