Equation 677 Database

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Magma f64f6356d3db…

magma f64f6356d3db
Size
595
Isomorphism class hash
f64f6356d3db7666d35a17104087c2f08d2d35aefb94b1c0139f39854dbc4e00
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 11:23:39
Display reorder
18,23,20,21,22,19,109,114,110,111,112,113,438,440,439,441,442,443,429,431,430,428,426,427,334,333,335,330,331,332,523,533,531,549,571,255,258,162,256,257,201,182,51,52,53,54,55,11,10,6,7,8,9,49,48,50,227,228,47,242,241,193,192,121,122,165,164,166,167,168,266,208,267,209,268,206,207,214,170,215,171,216,172,191,108,104,105,106,107,359,358,357,356,354,355,497,496,495,494,493,492,397,396,398,400,401,399,421,420,422,423,424,425,502,501,503,498,499,500,348,350,349,353,351,352,466,465,467,464,462,463,540,546,534,536,532,535,526,559,550,573,569,557,592,568,565,589,64,63,65,60,61,62,81,80,82,83,84,79,150,149,151,152,153,148,138,137,139,140,141,136,128,127,123,124,125,126,155,154,156,157,158,247,239,97,237,238,188,189,234,233,75,235,232,185,190,99,100,101,102,98,361,360,362,364,365,363,324,326,325,327,328,329,318,320,319,321,322,323,384,386,385,389,387,388,286,285,287,283,282,284,475,476,474,479,477,478,504,509,506,508,505,507,539,527,510,522,516,513,547,560,583,575,579,566,585,574,558,556,89,88,90,85,86,87,0,5,1,2,3,4,74,73,69,70,71,72,115,120,116,117,118,119,32,31,33,34,35,30,146,145,147,144,143,274,280,169,281,277,272,273,276,279,103,278,275,240,220,29,25,26,27,28,418,417,419,415,416,414,411,413,412,408,409,410,379,378,380,382,383,381,293,292,291,289,290,288,302,301,300,304,305,303,481,482,480,485,483,484,343,342,344,347,345,346,538,542,519,525,520,521,524,548,561,552,572,594,582,555,586,563,129,134,130,131,132,133,36,224,180,225,179,223,178,177,221,175,222,176,231,183,184,66,67,68,57,56,58,59,229,230,142,245,246,198,197,269,211,271,213,270,210,212,261,204,259,202,260,203,205,265,262,163,263,264,309,311,310,306,307,308,299,298,297,296,294,295,402,404,403,405,406,407,437,436,435,433,434,432,376,375,377,372,373,374,457,456,458,459,460,461,313,312,314,317,315,316,541,545,529,528,530,518,512,581,551,576,570,593,580,591,590,577,17,16,12,13,14,15,159,249,250,160,251,248,174,173,219,217,24,218,236,187,186,76,77,78,38,37,39,40,181,226,244,243,194,195,196,135,43,42,44,45,46,41,92,91,93,94,95,96,161,200,252,253,254,199,394,393,395,391,392,390,340,339,341,337,338,336,453,455,454,450,451,452,366,368,367,371,369,370,486,487,488,489,490,491,444,446,445,449,447,448,472,471,473,470,468,469,537,543,511,514,515,517,544,587,554,567,584,562,578,588,564,553 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 {6, 12} (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 11:23:40 · history