$(2,m,n)$-groups with Euler characteristic equal to $-2^as^b$

(2, m, n)-groups with Euler characteristic equal to -2asb

We study those (2,m, n)-groups which are almost simple and for which the absolute value of the Euler characteristic is a product of two prime powers. All such groups which are not isomorphic to PSL2(q) or PGL2(q) are completely classified.

( 2 , m , n ) - groups with Euler characteristic equal to − 2 a s b Nick

We study those (2,m, n)-groups which are almost simple and for which the absolute value of the Euler characteristic is a product of two prime powers. All such groups which are not isomorphic to PSL2(q) or PGL2(q) are completely classified.

On the Euler characteristic of definable groups

We show that in an arbitrary o-minimal structure the following are equivalent: (i) conjugates of a definable subgroup of a definably connected, definably compact definable group cover the group if the o-minimal Euler characteristic of the quotient is non zero; (ii) every infinite, definably connected, definably compact definable group has a non trivial torsion point. ∗The author was supported b...

The Euler characteristic of definable groups

We show that in an arbitrary o-minimal structure the following are equivalent: (i) every infinite, definably compact, definably connected definable group G has o-minimal Euler characteristic E(G) zero; (ii) if H is a definable subgroup of a definably compact, definably connected, definable group G such that E(G/H) 6= 0, then G = ∪{gHg−1 : g ∈ G}; (iii) every infinite, definably compact, definab...

Exponentiation and Euler Characteristic