Equation 677 Database

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Magma f8bbcb9803d8…

magma f8bbcb9803d8
Size
595
Isomorphism class hash
f8bbcb9803d8f7e0a383ef2e8fb3dedb6be66d69d21b08e2d11b48c9ef5dfcc3
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 10:05:17
Display reorder
59,58,57,56,54,55,158,157,156,161,159,160,98,97,96,99,100,101,359,358,354,355,356,357,375,374,376,377,372,373,536,517,524,557,589,165,166,162,163,164,167,118,117,119,116,114,115,173,172,171,170,168,169,178,177,179,176,174,175,195,191,187,183,256,253,200,199,198,196,197,249,242,241,240,239,237,238,0,1,2,3,4,5,351,350,352,353,348,349,287,286,282,283,284,285,424,423,425,420,421,422,473,472,468,469,470,471,365,364,360,361,362,363,435,434,436,437,432,433,407,406,402,403,404,405,291,290,292,293,288,289,539,510,551,538,537,544,543,527,585,584,586,569,593,571,563,556,217,218,214,215,213,216,244,243,245,248,246,247,250,254,180,189,193,185,44,43,42,39,40,41,109,108,110,112,113,111,22,21,23,26,24,25,93,95,94,90,91,92,227,226,225,229,230,228,484,483,485,480,481,482,415,414,416,417,418,419,451,450,452,453,454,455,504,509,505,506,507,508,386,385,387,388,389,384,323,322,318,319,320,321,302,301,303,304,305,300,334,333,335,330,331,332,516,549,523,540,547,513,526,552,591,581,587,565,576,566,578,564,78,79,81,82,83,80,154,153,155,152,150,151,140,139,138,137,135,136,63,65,64,61,62,60,28,27,29,31,32,30,105,107,106,103,104,102,10,9,11,7,8,6,66,68,67,71,69,70,379,378,380,381,382,383,445,444,446,447,448,449,478,477,479,474,475,476,297,296,298,299,294,295,503,502,498,499,500,501,465,464,466,467,462,463,263,262,259,258,260,261,412,411,413,408,409,410,528,519,511,532,521,525,514,535,594,561,562,570,579,590,577,575,235,236,232,233,231,234,219,221,220,223,224,222,252,257,181,190,194,186,53,52,51,120,121,122,35,34,33,38,36,37,87,89,88,85,86,84,20,19,18,17,16,15,127,126,128,143,141,142,345,344,346,347,342,343,393,392,394,395,390,391,315,314,316,317,312,313,337,336,338,339,340,341,491,490,486,487,488,489,325,324,326,327,328,329,273,272,274,275,270,271,265,264,266,267,268,269,529,533,512,541,550,522,515,548,592,560,580,558,567,588,559,583,147,148,144,145,146,149,125,124,123,14,12,13,45,47,46,48,49,50,76,75,77,74,72,73,192,188,184,182,255,251,211,210,212,209,207,208,204,206,205,201,202,203,129,131,130,134,132,133,281,280,276,277,278,279,457,456,458,459,460,461,492,497,493,494,495,496,308,307,309,310,311,306,401,400,396,397,398,399,438,443,439,440,441,442,369,368,370,371,366,367,430,429,431,426,427,428,520,531,545,518,534,546,542,530,553,574,554,573,555,568,572,582 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 {24, 30} (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 10:05:21 · history