Abstract
Let G be a finite group. The real genus p(G) is the minimum algebraic genus of any compact bordered Klein surface on which G acts. We show that a non-cyclic p-group G has real genus not congruent to (1 — p3) (mod 2p3) if and only if G is in one of 14 families of groups. The genus formula for each of these 14 families of groups is determined. A consequence of this classification is that almost all positive integers that are the real genus of a p-group are congruent to (1 p3) (mod 2p3). Finally, the integers that occur as the real genus of a p-group with Frattini-class 2 have density zero in the positive integers.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Mathematical Proceedings of the Royal Irish Academy
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
