A note on a class of factorized p -groups

Enrico Jabara

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 4, page 993-996
  • ISSN: 0011-4642

Abstract

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In this note we study finite p -groups G = A B 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 2 n .

How to cite

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Jabara, Enrico. "A note on a class of factorized $p$-groups." Czechoslovak Mathematical Journal 55.4 (2005): 993-996. <http://eudml.org/doc/31005>.

@article{Jabara2005,
abstract = {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 $2n$.},
author = {Jabara, Enrico},
journal = {Czechoslovak Mathematical Journal},
keywords = {factorizable groups; products of subgroups; $p$-groups; factorizable groups; products of subgroups; finite -groups; derived lengths},
language = {eng},
number = {4},
pages = {993-996},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on a class of factorized $p$-groups},
url = {http://eudml.org/doc/31005},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Jabara, Enrico
TI - A note on a class of factorized $p$-groups
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 993
EP - 996
AB - 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 $2n$.
LA - eng
KW - factorizable groups; products of subgroups; $p$-groups; factorizable groups; products of subgroups; finite -groups; derived lengths
UR - http://eudml.org/doc/31005
ER -

References

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  1. Products of Groups, Clarendon Press, Oxford, 1992. (1992) MR1211633
  2. 10.1112/S0024609397004050, Bull. London Math. Soc. 30 (1998), 247–250. (1998) MR1608098DOI10.1112/S0024609397004050
  3. 10.1006/jabr.1998.8045, J.  Algebra 224 (2000), 263–267. (2000) Zbl0953.20008MR1739580DOI10.1006/jabr.1998.8045
  4. A note on factorized (finite) groups, Rend. Sem. Mat. Padova 98 (1997), 101–105. (1997) MR1492971
  5. 10.1007/BF01219093, Math. Z. 134 (1973), 81–83. (1973) MR0325764DOI10.1007/BF01219093

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