Equation 677 Database

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Magma 9d92ea0bec9e…

magma 9d92ea0bec9e
Size
595
Isomorphism class hash
9d92ea0bec9e63eef1f85c5585350410c44b6bdb38c0063317c69f2e2b031ce8
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
2026-10-06 11:20:04
Display reorder
300,301,302,304,305,303,461,460,456,457,458,459,451,450,452,453,454,455,509,508,505,504,506,507,441,440,442,443,438,439,555,592,593,594,591,175,174,177,178,176,173,17,16,15,12,13,14,208,207,206,204,205,203,193,192,191,196,194,195,186,185,187,189,190,188,19,18,20,22,23,21,102,104,103,106,107,105,197,199,198,200,201,202,10,9,11,6,7,8,183,182,184,181,179,180,358,357,359,354,355,356,470,469,471,472,473,468,417,416,418,419,414,415,429,428,430,431,427,426,347,346,342,343,344,345,352,351,353,348,349,350,537,536,524,523,551,541,525,540,510,556,567,580,583,588,568,574,25,24,27,28,29,26,128,130,129,126,127,125,137,139,138,142,140,141,144,143,145,147,148,146,36,38,37,39,40,41,133,132,131,136,134,135,113,112,111,108,109,110,118,209,117,116,114,115,124,123,122,120,121,119,33,35,34,31,32,30,371,370,366,367,368,369,479,478,474,475,476,477,396,397,398,399,400,401,463,462,464,465,466,467,372,377,373,374,375,376,365,364,360,361,362,363,527,526,512,511,547,546,520,545,519,559,563,579,581,587,564,573,250,249,246,247,248,251,219,221,220,217,218,216,288,289,290,291,292,293,230,229,228,233,231,232,244,243,245,241,242,240,224,223,222,227,225,226,65,64,63,60,61,62,294,295,296,298,299,297,215,214,213,211,212,210,235,234,236,239,237,238,329,328,324,325,326,327,490,489,491,486,487,488,424,423,425,420,421,422,481,480,482,483,484,485,330,335,331,332,333,334,323,322,318,319,320,321,532,533,534,535,548,549,531,550,528,560,566,577,582,586,565,571,164,166,163,161,162,165,261,263,262,259,260,258,270,272,271,275,273,274,277,276,278,280,281,279,158,160,159,155,156,157,266,265,264,269,267,268,152,154,153,150,151,149,284,283,282,287,285,286,257,256,255,253,254,252,169,168,167,170,171,172,379,378,380,381,382,383,498,503,499,500,501,502,410,409,411,412,413,408,493,492,494,495,496,497,386,385,387,388,389,384,391,390,392,393,394,395,539,538,521,522,553,554,530,552,529,558,569,576,584,589,570,575,87,89,86,84,85,88,73,72,74,77,75,76,45,47,46,44,42,43,52,51,53,49,50,48,101,100,99,98,96,97,81,83,82,78,79,80,1,2,0,4,5,3,59,58,57,56,54,55,66,68,67,71,69,70,92,91,90,93,94,95,316,315,317,312,313,314,436,435,437,432,433,434,402,407,403,404,405,406,447,446,448,449,444,445,338,337,339,340,341,336,307,311,306,308,309,310,514,517,518,516,542,544,513,543,515,557,561,578,585,590,562,572 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#53d992532d406ee1a16d046074f6b11dc06c8f5c6df8c27dc9277719dd794878, M = the submagma generated by {60, 72} (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 2026-10-06 11:20:05 · history