NEW LOWER BOUNDS FOR THE NUMBER OF CONJUGACY CLASSES IN FINITE NILPOTENT GROUPS

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BERTRAM EDWARD A.

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2022 | Volume:11 | Issue:2 Page(s): 109-119

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Title

NEW LOWER BOUNDS FOR THE NUMBER OF CONJUGACY CLASSES IN FINITE NILPOTENT GROUPS

Author(s)

BERTRAM EDWARD A. | Issue Writer Certificate

Keywords

Nilpotent

conjugacy

derived series

Abstract

P. Hall's classical equality for the number of conjugacy classes in p-groups yields k(G) ,(3=2) log2 jGj when G is nilpotent. Using only Hall's theorem, this is the best one can do when jGj = 2. Using a result of G. J. Sherman, we improve the constant 3=2 to 5=3, which is best possible across all nilpotent groups and to 15=8 when G is nilpotent and jGj n 6= 8,16. These results are then used to prove that k(G) > log3 (jGj) when G=N is nilpotent, under natural conditions on N E G. Also, when G 0 is nilpotent of class c, we prove that k(G) ,(log jGj) t when jGj is large enough, depending only on (c,t).

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APA: Copy

BERTRAM, EDWARD A.. (2022). NEW LOWER BOUNDS FOR THE NUMBER OF CONJUGACY CLASSES IN FINITE NILPOTENT GROUPS. INTERNATIONAL JOURNAL OF GROUP THEORY, 11(2), 109-119. SID. https://sid.ir/paper/1004118/en

Vancouver: Copy

BERTRAM EDWARD A.. NEW LOWER BOUNDS FOR THE NUMBER OF CONJUGACY CLASSES IN FINITE NILPOTENT GROUPS. INTERNATIONAL JOURNAL OF GROUP THEORY[Internet]. 2022;11(2):109-119. Available from: https://sid.ir/paper/1004118/en

IEEE: Copy

EDWARD A. BERTRAM, “NEW LOWER BOUNDS FOR THE NUMBER OF CONJUGACY CLASSES IN FINITE NILPOTENT GROUPS,” INTERNATIONAL JOURNAL OF GROUP THEORY, vol. 11, no. 2, pp. 109–119, 2022, [Online]. Available: https://sid.ir/paper/1004118/en

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