Equation 677 Database

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Magma 1d6ad8fb74f2…

magma 1d6ad8fb74f2
Size
595
Isomorphism class hash
1d6ad8fb74f2bb6554ab5693578c254e577f88144eb1f03dfc752d155ccedff2
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 11:07:24
Display reorder
117,116,118,113,114,115,111,110,112,107,108,109,137,136,138,139,134,135,366,368,367,369,370,371,284,283,282,286,287,285,540,531,575,585,572,245,244,174,241,242,243,161,121,123,119,120,122,79,78,74,75,76,77,132,131,133,212,213,163,178,177,179,150,16,17,27,31,28,29,30,183,169,227,228,229,226,170,204,203,205,160,206,207,479,478,477,476,474,475,500,502,501,497,498,499,458,457,456,461,459,460,428,427,426,430,431,429,492,491,493,494,495,496,288,290,289,293,291,292,400,399,401,396,397,398,347,346,345,342,343,344,549,550,513,521,536,537,522,535,580,559,562,577,566,589,563,593,49,48,50,45,46,47,38,37,34,35,36,33,10,15,11,12,13,14,70,69,71,72,73,68,90,89,91,92,93,94,65,64,66,67,63,188,215,165,216,217,214,164,237,236,171,233,234,235,503,490,489,488,486,487,297,299,298,294,295,296,301,300,302,304,305,303,507,506,505,504,509,508,471,473,472,470,468,469,313,312,314,315,316,317,320,319,318,322,323,321,386,385,384,387,388,389,526,525,520,548,551,518,523,511,560,573,568,574,567,582,581,565,100,99,95,96,97,98,53,52,55,56,51,54,21,26,22,23,24,25,39,44,40,41,42,43,127,126,128,129,124,125,146,145,147,148,149,257,250,247,251,252,253,232,248,249,246,254,255,256,365,364,363,362,360,361,380,379,378,383,381,382,447,449,448,444,445,446,464,463,462,466,467,465,355,354,356,357,358,359,310,309,311,306,307,308,441,443,442,440,438,439,390,392,391,394,395,393,541,534,512,516,515,517,519,514,553,594,578,555,588,591,554,576,59,58,60,61,62,57,32,187,185,186,152,184,189,154,190,153,191,192,181,180,151,18,19,20,142,141,143,144,230,231,173,182,239,240,172,238,155,193,194,195,196,156,225,224,221,168,222,223,265,264,266,268,269,267,263,262,261,260,259,258,274,273,275,271,272,270,373,372,374,375,376,377,403,402,404,405,406,407,280,279,281,276,277,278,484,483,485,481,480,482,353,352,351,348,349,350,547,545,539,528,530,529,510,527,552,592,590,557,587,561,558,556,86,85,87,88,83,84,130,211,209,162,210,208,200,158,201,202,159,199,198,197,157,81,82,80,7,6,8,9,176,175,219,218,166,220,167,140,2,0,3,4,5,1,106,105,101,102,103,104,425,424,423,422,420,421,451,450,452,454,455,453,416,415,414,419,417,418,434,433,432,436,437,435,334,333,335,330,331,332,411,413,412,410,408,409,324,326,325,329,327,328,340,339,341,338,336,337,538,524,543,546,544,533,532,542,564,586,570,579,571,569,583,584 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#40b1db721c17bf32e266eb97cd1492697125779c7804a195f580e3a793b1a85e, M = the submagma generated by {24, 54} (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 11:07:26 · history