Abstract
The family \(G(m,n)=\langle x,y| x^2=(xy^2)^2=1,~y^{2^m}=(xy)^{2^{n}}\rangle \) of finite 2-groups will be introduced. The group G(m, n) has order \(2^{(m+n+1)}\), nilpotency class \(1+\max \{m,n\}\) and every automorphism of \(G=G(m,n)\) fixes \(G/\varPhi (G)\) elementwise and therefore Aut(G) is a 2-group. The parameterized presentation of \(G=G(m,n)\) is efficient as the Schur multiplicator of G is non-trivial.
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Abdolzadeh, H., Sabzchi, R. (2018). A Class of Finite 2-groups G with Every Automorphism Fixing \(G/\varPhi (G)\) Elementwise. In: Badawi, A., Vedadi, M., Yassemi, S., Yousefian Darani, A. (eds) Homological and Combinatorial Methods in Algebra. SAA 2016. Springer Proceedings in Mathematics & Statistics, vol 228. Springer, Cham. https://doi.org/10.1007/978-3-319-74195-6_7
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DOI: https://doi.org/10.1007/978-3-319-74195-6_7
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