The genesis of this paper is a talk that I gave to a non-mathematical audience in October 2007. T... more The genesis of this paper is a talk that I gave to a non-mathematical audience in October 2007. The audience was primarily faculty members in the College of Liberal Arts at Towson University. Many of the faculty confided to me that they were afraid of mathematics and not very good at it. The response to the talk was very positive and everyone felt that they got something out of it. A PowerPoint presentation of the talk is available at [5]. The talk should begin with a description of what we are going to do. Specifically, a group is a mathematical object like a number system. This part was held to a minimum. The concept of symmetry was discussed next. The members of the audience were given a set of cardboard equilateral triangles and pieces of paper with a slightly larger equilateral triangle drawn on it (as shown in Figure 1). The question was posed, how many symmetries of this equilateral triangle are there? The most common answers to this question by college students are three, fi...
Proceedings of the American Mathematical Society, 1986
We prove that if G G is a group such that Aut G G is a countably infinite torsion F C FC -group, ... more We prove that if G G is a group such that Aut G G is a countably infinite torsion F C FC -group, then Aut G G contains an infinite locally soluble, normal subgroup and hence a nontrivial abelian normal subgroup. It follows that a countably infinite subdirect product of nontrivial finite groups, of which only finitely many have nontrivial abelian normal subgroups, is not the automorphism group of any group.
The object of this paper is to exhibit an infinite set of finite semisimple groups H, each of whi... more The object of this paper is to exhibit an infinite set of finite semisimple groups H, each of which is the automorphism group of some infinite group, but of no finite group. We begin the construction by choosing a finite simple group S whose outer automorphism group and Schur multiplier possess certain specified properties. The group H is a certain subgroup of Aut S which contains S. For example, most of the PSL's over a non-prime finite field are candidates for S, and in this case, H is generated by all of the inner, diagonal and graph automorphisms of S.
The genesis of this paper is a talk that I gave to a non-mathematical audience in October 2007. T... more The genesis of this paper is a talk that I gave to a non-mathematical audience in October 2007. The audience was primarily faculty members in the College of Liberal Arts at Towson University. Many of the faculty confided to me that they were afraid of mathematics and not very good at it. The response to the talk was very positive and everyone felt that they got something out of it. A PowerPoint presentation of the talk is available at [5]. The talk should begin with a description of what we are going to do. Specifically, a group is a mathematical object like a number system. This part was held to a minimum. The concept of symmetry was discussed next. The members of the audience were given a set of cardboard equilateral triangles and pieces of paper with a slightly larger equilateral triangle drawn on it (as shown in Figure 1). The question was posed, how many symmetries of this equilateral triangle are there? The most common answers to this question by college students are three, fi...
Proceedings of the American Mathematical Society, 1986
We prove that if G G is a group such that Aut G G is a countably infinite torsion F C FC -group, ... more We prove that if G G is a group such that Aut G G is a countably infinite torsion F C FC -group, then Aut G G contains an infinite locally soluble, normal subgroup and hence a nontrivial abelian normal subgroup. It follows that a countably infinite subdirect product of nontrivial finite groups, of which only finitely many have nontrivial abelian normal subgroups, is not the automorphism group of any group.
The object of this paper is to exhibit an infinite set of finite semisimple groups H, each of whi... more The object of this paper is to exhibit an infinite set of finite semisimple groups H, each of which is the automorphism group of some infinite group, but of no finite group. We begin the construction by choosing a finite simple group S whose outer automorphism group and Schur multiplier possess certain specified properties. The group H is a certain subgroup of Aut S which contains S. For example, most of the PSL's over a non-prime finite field are candidates for S, and in this case, H is generated by all of the inner, diagonal and graph automorphisms of S.
Uploads
Papers