-free
-groups
Abstract
If
is a lattice, a group is called
-free if its subgroup lattice has no sublattice isomorphic to
. It is easy to see that
, the subgroup lattice of the dihedral group of order 8, is the largest lattice
such that every finite
-free
-group is modular. In this paper we continue the study of
-free groups. We determine all finite
-free
-groups for primes
and
, except those of order
with normal Sylow
-subgroup
![L](http://212.189.136.205/plugins/generic/latexRender/cache/d20caec3b48a1eef164cb4ca81ba2587.png)
![L](http://212.189.136.205/plugins/generic/latexRender/cache/d20caec3b48a1eef164cb4ca81ba2587.png)
![L](http://212.189.136.205/plugins/generic/latexRender/cache/d20caec3b48a1eef164cb4ca81ba2587.png)
![L_{10}](http://212.189.136.205/plugins/generic/latexRender/cache/2811b5c761be1f827045c7c70356bfea.png)
![L](http://212.189.136.205/plugins/generic/latexRender/cache/d20caec3b48a1eef164cb4ca81ba2587.png)
![L](http://212.189.136.205/plugins/generic/latexRender/cache/d20caec3b48a1eef164cb4ca81ba2587.png)
![p](http://212.189.136.205/plugins/generic/latexRender/cache/83878c91171338902e0fe0fb97a8c47a.png)
![L_{10}](http://212.189.136.205/plugins/generic/latexRender/cache/2811b5c761be1f827045c7c70356bfea.png)
![L_{10}](http://212.189.136.205/plugins/generic/latexRender/cache/2811b5c761be1f827045c7c70356bfea.png)
![\{p,q\}](http://212.189.136.205/plugins/generic/latexRender/cache/4fd88312d13befd446c375a8875bedf6.png)
![p](http://212.189.136.205/plugins/generic/latexRender/cache/83878c91171338902e0fe0fb97a8c47a.png)
![q](http://212.189.136.205/plugins/generic/latexRender/cache/7694f4a66316e53c8cdd9d9954bd611d.png)
![2^{\alpha}3^{\beta}](http://212.189.136.205/plugins/generic/latexRender/cache/52447c9b083eb2bc60667b7d667b73a3.png)
![3](http://212.189.136.205/plugins/generic/latexRender/cache/eccbc87e4b5ce2fe28308fd9f2a7baf3.png)
DOI Code:
10.1285/i15900932v30n1supplp55
Keywords:
subgroup lattice; sublattice; finite group; modular Sylow subgroup
Full Text: PDF