By Mark L. Lewis, Gabriel Navarro, Donald S. Passman, Thomas R. Wolf

ISBN-10: 0821848275

ISBN-13: 9780821848272

**Read Online or Download Character Theory of Finite Groups: Conference in Honor of I. Martin Isaacs, June 3-5, 2009, Universitat De Valencia, Valencia, Spain PDF**

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**Additional info for Character Theory of Finite Groups: Conference in Honor of I. Martin Isaacs, June 3-5, 2009, Universitat De Valencia, Valencia, Spain**

**Example text**

In the method described above, there is nothing particularly unique about Bπ (G) and the subnormal nucleus. In other words, one can obtain the same result by using the set Nπ (G) and the normal nucleus [3], or other similar constructions. For instance, in [9] a similar lower bound for the number of N -lifts is developed, and in [22] a similar result is obtained for generating lifts via objects called selfstabilizing pairs (deﬁned in [22]). 2. Upper bounds for the number of lifts in groups of odd order.

Assume ﬁnally that 0 ≤ j1 , j2 < n1/4 . The corresponding terms are bounded by 3 5 3 2 + cos 5 5 2πj1 n 2 + cos 5 2πj2 n 1/2 2cn2 2 −cn2 5 ≤e ≤ e− Since e− c16π 2 25 c16π 2 25 2πj1 n 2 +5 2πj2 n 2 (j12 +j22 ) . (j12 +j22 ) 1≤j1 <∞, 0≤j2 <∞ converges, and tends to zero as c → ∞, we have proved the upper bound in the 2 following theorem. 1. 4. For n ≥ 5 and c > 0, the random walk on Cn2 generated by {0, ±1, ±n} after k = cn2 steps satisﬁes L(c) ≤ Q∗k − U ≤ U (c) with positive continuous functions L(c), U (c) such that U (c) → 0 as c → ∞.

Navarro, Characters and Blocks of Finite Groups, Cambridge University Press, 1998. [26] G. Navarro, A new character correspondence in groups of odd order, Journal of Algebra 268 (2003), 8-21. [27] G. Navarro, New properties of the π-special characters, Journal of Algebra 187 (1997), 203213. [28] G. Navarro, Vertices for characters of p-solvable groups, Transactions of the American Mathematical Society 354 (2002) 2759-2773. [29] G. Navarro, Weights, vertices, and a correspondence of characters in groups of odd order, Mathematische Zeitschrift 212 (1993), 535-544.

### Character Theory of Finite Groups: Conference in Honor of I. Martin Isaacs, June 3-5, 2009, Universitat De Valencia, Valencia, Spain by Mark L. Lewis, Gabriel Navarro, Donald S. Passman, Thomas R. Wolf

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