Equation 677 Database

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Magma ad44afeac7f6…

magma ad44afeac7f6
Size
595
Isomorphism class hash
ad44afeac7f6a2fa09bf491eda882adaa5e52c9d665baadc0a39a8bbef6102eb
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 23:45:43
Display reorder
347,345,350,348,349,346,282,281,398,283,284,285,303,304,399,305,306,307,352,411,351,354,355,353,243,242,244,245,240,241,518,515,514,534,590,494,495,402,492,493,457,452,381,380,382,383,384,386,388,387,385,426,424,421,420,419,501,502,418,470,469,436,435,343,344,370,400,371,369,368,500,440,473,441,474,460,442,109,108,110,111,112,113,120,125,121,122,123,124,52,51,53,48,49,50,38,37,39,40,41,36,76,75,77,72,73,74,166,165,167,162,163,164,8,7,9,10,11,6,219,218,220,221,216,217,152,151,153,154,155,150,540,544,511,524,525,532,536,551,570,560,554,568,561,557,556,586,287,286,288,291,289,290,376,375,377,373,374,372,365,367,366,363,364,362,322,321,320,325,323,324,326,328,327,329,330,331,278,277,276,279,280,465,466,292,467,468,434,433,213,212,214,215,210,211,161,160,156,157,158,159,16,15,17,12,13,14,223,222,224,225,226,227,255,254,256,257,252,253,116,115,117,118,119,114,81,80,82,83,78,79,264,269,265,266,267,268,146,145,147,148,149,144,513,537,538,539,521,523,545,587,585,584,583,567,569,592,566,594,299,298,410,300,301,302,339,338,337,342,340,341,297,296,295,293,412,294,314,316,315,317,318,319,313,312,311,310,308,309,430,429,428,431,432,509,507,427,506,508,504,505,259,258,260,261,262,263,31,30,32,33,34,35,98,97,99,100,101,96,85,84,86,87,88,89,247,246,248,249,250,251,234,239,235,236,237,238,42,47,43,44,45,46,29,28,24,25,26,27,231,230,232,233,228,229,519,548,546,517,547,520,516,558,589,593,582,588,550,591,552,549,336,403,335,332,333,334,417,499,459,497,461,498,439,462,472,437,471,438,484,454,453,393,394,395,391,390,392,389,483,482,401,489,490,456,455,491,443,475,444,476,445,446,191,190,186,187,188,189,196,195,197,193,192,194,105,104,106,107,102,103,271,270,272,273,274,275,56,55,57,58,59,54,19,18,20,21,22,23,203,202,198,199,200,201,68,67,69,70,71,66,142,141,143,138,139,140,535,542,531,526,527,510,512,563,564,578,559,565,577,553,579,555,359,361,360,357,358,356,396,486,485,397,487,488,451,450,479,480,379,481,503,463,464,423,425,422,416,415,414,413,458,496,478,477,447,449,448,378,404,406,405,407,408,409,93,92,94,95,90,91,4,3,5,1,0,2,127,126,128,129,130,131,137,136,132,133,134,135,177,176,178,179,174,175,208,207,209,204,205,206,183,182,184,185,180,181,61,60,62,63,64,65,168,173,169,170,171,172,533,528,529,522,530,541,543,581,580,573,571,572,562,575,576,574 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#21508ce76d8339c8cc8a9db508194b7933fb8eb19570d11d640cb6bc14178d14, M = the submagma generated by {0, 36} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 23:45:44 · history