ELISA (Extending LIfting Subgroup Algorithms) 

Version 1.1

Authors: Septimiu Crivei, Gabriela Olteanu and Stefan Suteu Szollosi 
 

Email addresses: crivei at math.ubbcluj.ro, golteanu at um.es, szollosi at gmail.com

 

Date: 25-09-2007

  

I. Introduction
  
---------------
  
  	

ELISA is a collection of functions able to determine some properties of finite abelian
 (sub)groups, namely those listed at II. As it can be seen, the notions below involve heavily
 (alongside the obviously required inclusion relation) operations like subgroup intersection 
and addition. These functions work at the level of readily built subgroup lattice and (in 
most of the cases) they avoid computing directly with the subgroups (via their elements).
 The subgroup lattice is regarded instead as a directed graph and the computations are carried
 out only based on the information retrievable from the constructed subgroup lattice (i.e. the 
maximal subgroup and minimal supergroup relations).
 

 

II. List of new notions treated in Version 1.1:
 
----------------------------------------------- 

- orthogonal groups
- parallel groups
- type subgroups
- TS groups

In the sequel G, G1, G2 denote finite abelian groups and A a subgroup of G.



III. List of new implemented functions:

---------------------------------------



* AreOrthogonal( G1, G2 )
	
Returns true if the groups G1 and G2 are orthogonal, false otherwise.
	
File: AreOrthogonal.g

	

* AreParallel( G1, G2 )
	
Returns true if the groups G1 and G2 are parallel, false otherwise.
	
File: AreParallel.g



* TypeSubgroups( G )
Returns a list of all type subgroups of G.
File: TypeSubgroups.g

* IsTypeSubgroup( G, A )
Returns true if A is a type subgroup of G, false otherwise.

File: IsTypeSubgroup.g

* IsTS( G )
Returns true if G is a TS group, false otherwise.



As it can be seen, there are functions requiring other functions to be loaded. For your convenience there is
 the file named "elisa2.g" which contains all the functions of the first release of ELISA as well as the new ones in Version 1.1. Read this file in GAP if you plan to use many (or all the) functions.

 

IV. Feedback, bug reports
 
-------------------------
 	

Please note that this is a work in progress and changes or completions might appear in the future.
 Any feedback, questions or bug reports are welcome; contact szollosi at gmail.com or crivei at math.ubbcluj.ro
 	
  

V. License
  
----------

    

This collection of functions (ELISA and its Version 1.1) is distributed under GNU GPL license.
 
Copyright (C) 2006-2007 S. Crivei, G. Olteanu, S. Szollosi

    

This program is free software; you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation; either version 2 of the License, or
 (at your option) any later version.

 

This program is distributed in the hope that it will be useful,
 but WITHOUT ANY WARRANTY; without even the implied warranty of
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 GNU General Public License for more details.

 

You should have received a copy of the GNU General Public License
 along with this program; if not, write to the Free Software
 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA