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Problem 1160 — Erdős Problems

Problem 1160

Let $g(n)$ denote the number of groups of order $n$ . If $n\leq 2^m$ then $g(n)\leq g(2^m)$ .

Source: erdosproblems.com/1160

Group theory

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No claim settles this problem.

Open. The site's commentary credits Pantelidakis [Pa03] with the case of odd $n$ and $m\ge3619$ , recorded as a pending partial claim on its claim page (Pantelidakis, 2003); it does not change the standing.

BNV07: Blackburn, Simon R. and Neumann, Peter M. and Venkataraman, Geetha, Enumeration of finite groups. (2007), xii+281.
Pa03: I. Pantelidakis, On the Number of Non-isomorphic Groups of the Same Order. DPhil Thesis, University of Oxford (2003).

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Status: Open
Topics: Group theory
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