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Kaur, Dilpreet
- Characters of Real Special 2-Groups
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1 Indian Institute of Science Education and Research, Knowledge City, Sector-81, Mohali-140306, IN
1 Indian Institute of Science Education and Research, Knowledge City, Sector-81, Mohali-140306, IN
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Journal of the Ramanujan Mathematical Society, Vol 30, No 4 (2015), Pagination: 375-396Abstract
It is well-known that special 2-groups can be described in terms of quadratic maps over fields of characteristic 2. In this article we develop methods to compute conjugacy classes, complex representations and characters of a real special 2-group using quadratic maps alone.
- 𝓏-Classes and Rational Conjugacy Classes in Alternating Groups
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1 IISER Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, IN
1 IISER Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, IN
Source
Journal of the Ramanujan Mathematical Society, Vol 34, No 2 (2019), Pagination: 169-183Abstract
In this paper, we compute the number of z-classes (conjugacy classes of centralizers of elements) in the symmetric group Sn, when n ≥ 3 and alternating group An when n ≥ 4. It turns out that the difference between the number of conjugacy classes and the number of z-classes for Sn is determined by those restricted partitions of n − 2 in which 1 and 2 do not appear as its part. In the case of alternating groups, it is determined by those restricted partitions of n −3 which has all its parts distinct, odd and in which 1 (and 2) does not appear as its part, along with an error term. The error term is given by those partitions of n which have distinct parts that are odd and perfect squares. Further, we prove that the number of rational-valued irreducible complex characters for An is same as the number of conjugacy classes which are rational.References
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