GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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%A  autpgrp.tex        AutPGrp documentation                 Bettina Eick
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%A                                                         Eamonn O'Brien
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\Chapter{Introduction}
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Given an arbitrary finite group, the computation of its automorphism
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group is a very difficult task. Pioneer work in this area was carried 
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out by Felsch \&  Neub{\accent127u}ser (1970), whose algorithm used 
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the output of their subgroup lattice program. A technique developed 
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by Neub{\accent127u}ser in the early 1970s sought to compute the 
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automorphism group viewed as a permutation group acting on unions of 
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certain conjugacy classes of the group. A similar method was implemented 
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by Hulpke (1997) in the {\GAP}~4 library. Recently, Cannon \& Holt (1999) 
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presented a new algorithm which uses a ``hybrid group'' approach. 
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More efficient approaches are available to determine the automorphism 
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group for groups satisfying certain properties. Following the work of 
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Shoda (1928), Hulpke in 1997 implemented a practical method for finite 
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abelian groups in the {\GAP}~4 library. Wursthorn (1993) adapted modular 
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group algebra techniques to compute the automorphism groups of $p$-groups; 
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the {\GAP}~3 share package \package{Sisyphos} includes an implementation. Smith 
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(1994) introduced an algorithm for finite solvable groups which is 
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available in the \package{AutAg} share package of {\GAP}~3. 
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Moreover, the $p$-group generation method of Newman (1977) and O'Brien 
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(1990) can be modified to compute the automorphism group of a finite 
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$p$-group as outlined in O'Brien (1995). This algorithm is implemented 
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in the ANU `pq' C program. 
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Here we introduce a new function to compute the automorphism group of 
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a finite $p$-group. The underlying algorithm is a refinement of the
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methods described in O'Brien (1995). In particular, this implementation
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is more efficient in both time and space requirements and hence has a 
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wider range of applications than the ANU `pq' method. Our package is 
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written in {\GAP} code and it makes use of a number of methods from the 
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{\GAP} library such as the MeatAxe for matrix groups and 
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permutation group functions. 
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The {\GAP}~4 package \package{ANUPQ}, which is an interface to most of
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the functionality of the ANU `pq' C program, uses the {\AutPGrp} package
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to compute automorphism groups of $p$-groups.
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We have compared our method to the others available in {\GAP}.
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Our package usually out-performs all but the method designed 
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for finite abelian groups. We note that our method uses the 
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small groups library in certain cases and hence our algorithm
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is more effective if the small groups library is installed.
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A {\GAP}~3 version of the methods implemented in this package 
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is available via 
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\URL{http://www-public.tu-bs.de:8080/~beick/so.html}
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