Rigidity of symmetric simplicial complexes and the lower bound theorem by James Cruickshank, Bill Jackson, Shin-ichi Tanigawa

“…Our result implies that Stanley’s lower bound theorem for centrally symmetric polytopes extends to pseudomanifolds with a free simplicial automorphism of order 2, thus verifying (the inequality part of) another conjecture of Klee, Nevo, Novik and Zheng. …”
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Orthogonal and oriented Fano planes, triangular embeddings of $ K_7, $ and geometrical representations of the Frobenius group $ F_{21} $ by Simone Costa, Marco Pavone

“…The main focus is on investigating the group of common automorphisms of two orthogonal Fano planes and the automorphism group of a suitably oriented Fano plane. …”
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Sectional and Ricci Curvature for Three-Dimensional Lie Groups by Gerard Thompson, Giriraj Bhattarai

“…In each case the metric is reduced by using the automorphism group of the associated Lie algebra. In particular, the maximum and minimum values of the sectional curvature function are determined.…”
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On Classical Quotient Rings of Skew Armendariz Rings by A. R. Nasr-Isfahani, A. Moussavi

“…Let R be a ring, α an automorphism, and δ an α-derivation of R. If the classical quotient ring Q of R exists, then R is weak α-skew Armendariz if and only if Q is weak α˜-skew Armendariz.…”
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The four known biplanes with k=11 by Chester J. Salwach, Joseph A. Mezzaroba

“…The four known biplanes of order 9(k=11) are described in terms of their ovals, λ-chain structures, and automorphism groups. An exhaustive computer search for all biplanes of order 9 with certain chain structures has produced but two, one of which is new. …”
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Projective varieties have countably many real forms by Labinet, Timothée L.

“…The verification consists in gathering known results about automorphism groups and Galois cohomology. This contrasts with the recent discovery by A. …”
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Prime Ideals and Strongly Prime Ideals of Skew Laurent Polynomial Rings by E. Hashemi

“…We first study connections between α-compatible ideals of R and related ideals of the skew Laurent polynomials ring R[x,x−1;α], where α is an automorphism of R. Also we investigate the relationship of P(R) and Nr(R) of R with the prime radical and the upper nil radical of the skew Laurent polynomial rings. …”
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An Extension of the Spectral Mapping Theorem by A. R. Medghalchi, S. M. Tabatabaie

“…We give an extension of the spectral mapping theorem on hypergroups and prove that if 𝐾 is a commutative strong hypergroup with 0𝑥0005𝑒𝐾=𝑋𝑏(𝐾) and 𝜅 is a weakly continuous representation of 𝑀(𝐾) on a 𝑊∗-algebra such that for every 𝑡∈𝐾, 𝜅𝑡 is an ∗-automorphism, 𝑠𝑝𝜅 is a synthesis set for 𝐿1(𝐾) and 𝜅(𝐿1(𝐾)) is without order, then for any 𝜇 in a closed regular subalgebra of 𝑀(𝐾) containing 𝐿1(𝐾), 𝜎(𝜅(𝜇))=0𝑥0005𝑒𝜇(𝑠𝑝𝜅), where 𝑠𝑝𝜅 is the Arveson spectrum of 𝜅.…”
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On generalized quaternion algebras by George Szeto

“…Let B be a commutative ring with 1, and G(={σ}) an automorphism group of B of order 2. The generalized quaternion ring extension B[j] over B is defined by S. …”
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The Concentration Function Problem for Locally Compact Groups Revisited: Nondissipating Space-Time Random Walks, -Decomposable Laws, and Their Continuous Time Analogues by Wilfried Hazod

“…It is closely related to discrete relatively compact M- or skew convolution semigroups and corresponding space-time random walks, and to -decomposable laws, respectively, where denotes an automorphism. Analogous results are obtained in the case of continuous time: nondissipating Lévy processes are related to relatively compact distributions of generalized Ornstein-Uhlenbeck processes and corresponding space-time processes and to -decomposable laws, respectively with denoting a continuous group of automorphisms acting as contracting mod. a compact subgroup.…”
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Fischer-Clifford Matrices and Character Table of the Maximal Subgroup (29:(L3(4)):2 of U6(2):2 by Abraham Love Prins, Ramotjaki Lucky Monaledi

“…The automorphism group U6(2):2 of the unitary group U6(2)≅Fi21 has a maximal subgroup G¯ of the form (29:(L3(4)):2 of order 20643840. …”
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Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum by Jia-Bao Liu, S. Morteza Mirafzal, Ali Zafari

“…Also, we determine the automorphism group of Γ. Moreover, we show that Γ and Kv▽Γ are determined by their spectrum.…”
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A cone conjecture for log Calabi-Yau surfaces by Jennifer Li

“…We prove that (1) the action of the automorphism group of $(Y_e,D_e)$ on its nef effective cone admits a rational polyhedral fundamental domain; and (2) the action of the monodromy group on the nef effective cone of a very general surface in the deformation type admits a rational polyhedral fundamental domain. …”
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On characterizations of a center Galois extension by George Szeto, Lianyong Xue

“…Let B be a ring with 1,  C the center of B,  G a finite automorphism group of B, and BG the set of elements in B fixed under each element in G. …”
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About permutations on the sets of tuples from elements of the finite field by V.S. Kugurakov, A.F. Gainutdinova, V.T. Dubrovin

“…The obtained results can be used to construct S-boxes and P-boxes in block ciphers and to calculate automorphism groups of error-correcting codes.…”
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Fraïssé limit via forcing by Mohammad Golshani

“…A Fra\"{i}ss\'{e} limit, denoted $Flim(\mathcal{K})$, of aFra\"{i}ss\'{e} class $\mathcal{K}$ is the unique\footnote{The existence and uniqueness follows from Fra\"{i}ss\'{e}'s theorem, See \cite{hodges}.} countable ultrahomogeneous (every isomorphism of finitely-generated substructures extends to an automorphism of $Flim(\mathcal{K})$) structure into which every member of $\mathcal{K}$ embeds.Given a Fraïssé class K and an infinite cardinal κ, we define a forcing notion which adds a structure of size κ using elements of K, which extends the Fraïssé construction in the case κ=ω.…”
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Genus 2 Seiberg-Witten curves for rank 2 N $$ \mathcal{N} $$ =4 superYang-Mills theories by Philip C. Argyres, Mario Martone, Zekai Yu

“…Abstract We determine new genus 2 Seiberg-Witten curves for four dimensional rank 2 absolute N $$ \mathcal{N} $$ =4 superYang-Mills theories using the automorphism twist approach. The conformal manifolds of these curves agree with those predicted by S-duality orbits of global structures, and we use this to identify which of the two S-duality orbits of the so 5 ≃ sp 4 $$ \mathfrak{so}(5)\simeq \mathfrak{sp}(4) $$ superYang-Mills theory the genus-2 curve corresponds to. …”
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Relations between the distinguishing number and some other graph parameters by Bahman Ahmadi, Seyed Alireza Talebpour Shirazi Fard

“…A distinguishing coloring of a simple graph $G$ is a vertex coloring of $G$ which is preserved only by the identity automorphism of $G$. In other words, this coloring ``breaks'' all symmetries of $G$. …”
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A characterization of $ b $-generalized skew derivations on a Lie ideal in a prime ring by Omaima Alshanqiti, Ashutosh Pandey, Mani Shankar Pandey

“…Assuming $ \Delta_1 $ and $ \Delta_2 $ are nontrivial $ \mathrm{b} $-generalized skew derivations associated with the same automorphism $ \alpha $, the paper aims to explore the detailed structure of these generalized derivations that satisfy the specific equation: \begin{document}$ p u \Delta_1(u) + \Delta_1(u) u q = \Delta_2(u^2), \ \text{with} \ p + q \notin \mathcal{C}, \; \; \text{for all } u \in \mathcal{L}. …”
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Bipartite Diametrical Graphs of Diameter 4 and Extreme Orders by Salah Al-Addasi, Hasan Al-Ezeh

“…Finally, we study some additional properties of 𝐺(2𝑚,2𝑚) concerning the order of its automorphism group, girth, domination number, and when being Eulerian.…”
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