Permutational and rewritable groups
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- by D. S. Passman
- Proc. Amer. Math. Soc. 147 (2019), 995-1003
- DOI: https://doi.org/10.1090/proc/14291
- Published electronically: November 8, 2018
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Abstract:
Permutational groups and rewritable groups were introduced in 1985 and 1988, respectively. In this note, we briefly survey key properties of these groups. In addition, we consider certain related parameters and we compute a number of examples of interest.References
- A. S. Amitsur and J. Levitzki, Minimal identities for algebras, Proc. Amer. Math. Soc. 1 (1950), 449–463. MR 36751, DOI 10.1090/S0002-9939-1950-0036751-9
- Russell D. Blyth, Rewriting products of group elements. I, J. Algebra 116 (1988), no. 2, 506–521. MR 953167, DOI 10.1016/0021-8693(88)90233-5
- Mario Curzio, Patrizia Longobardi, Mercede Maj, and Derek J. S. Robinson, A permutational property of groups, Arch. Math. (Basel) 44 (1985), no. 5, 385–389. MR 792360, DOI 10.1007/BF01229319
- M. I. Elashiry and D. S. Passman, Rewritable groups, J. Algebra 345 (2011), 190–201. MR 2842061, DOI 10.1016/j.jalgebra.2011.08.007
- I. Martin Isaacs, Character theory of finite groups, Dover Publications, Inc., New York, 1994. Corrected reprint of the 1976 original [Academic Press, New York; MR0460423 (57 #417)]. MR 1280461
- Irving Kaplansky, Groups with representations of bounded degree, Canad. J. Math. 1 (1949), 105–112. MR 28317, DOI 10.4153/cjm-1949-011-9
- D. S. Passman, Group rings satisfying a polynomial identity, J. Algebra 20 (1972), 103–117. MR 285631, DOI 10.1016/0021-8693(72)90091-9
Bibliographic Information
- D. S. Passman
- Affiliation: Department of Mathematics, University of Wisconsin–Madison, Madison, Wisconsin 53706
- MR Author ID: 136635
- Email: passman@math.wisc.edu
- Received by editor(s): January 8, 2018
- Received by editor(s) in revised form: June 16, 2018
- Published electronically: November 8, 2018
- Additional Notes: This research was supported in part by NSF grant DMS 1712663.
- Communicated by: Pham Huu Tiep
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 995-1003
- MSC (2010): Primary 20E25, 20B30, 16S34
- DOI: https://doi.org/10.1090/proc/14291
- MathSciNet review: 3896050