Equation 677 Database

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Magma 90ad3e5748c8…

magma 90ad3e5748c8
Size
381
Isomorphism class hash
90ad3e5748c8e557465675e645b1f009b50c26063871bffcc21c2a51f01c6fde
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:27:56
Display reorder
380,179,189,184,204,194,199,44,33,39,269,24,29,164,169,174,154,299,159,324,325,326,327,328,329,125,134,120,17,289,16,219,209,214,234,224,229,149,139,144,294,18,19,274,64,69,49,54,59,94,89,279,74,79,84,239,244,249,259,254,264,116,114,105,284,104,99,349,364,344,339,374,369,354,359,334,378,176,186,181,200,190,195,41,31,36,266,20,25,161,166,170,151,295,156,303,304,305,301,300,302,128,130,123,4,285,3,216,206,211,230,220,225,146,136,141,290,5,6,271,60,65,45,51,56,91,86,275,71,75,80,237,243,247,257,252,262,118,111,108,281,100,95,345,360,341,336,370,365,351,355,330,375,177,187,182,202,192,197,42,30,37,267,22,27,162,167,172,152,297,157,322,323,321,319,320,318,126,133,121,11,288,10,217,207,212,232,222,227,147,137,142,292,12,13,273,63,68,48,53,58,93,88,278,73,78,83,236,242,246,255,250,260,115,113,106,283,103,98,348,362,343,337,372,367,353,358,333,377,178,188,183,203,193,198,43,32,38,268,23,28,163,168,173,153,298,158,316,317,315,313,314,312,127,131,122,0,286,2,218,208,213,233,223,228,148,138,143,293,14,15,270,61,66,46,50,55,90,85,276,70,76,81,235,240,248,258,253,263,117,110,107,280,101,96,346,363,340,338,373,368,350,356,332,379,175,185,180,201,191,196,40,34,35,265,21,26,160,165,171,150,296,155,308,306,307,311,309,310,129,132,124,9,287,8,215,205,210,231,221,226,145,135,140,291,1,7,272,62,67,47,52,57,92,87,277,72,77,82,238,241,245,256,251,261,119,112,109,282,102,97,347,361,342,335,371,366,352,357,331,376 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#564914c332df918b1bab25ab6758cc0c591864f3f64c8c0ef251305010e22f83, M = {70} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:27:57 · history