Equation 677 Database

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Magma d3e8dfed9c49…

magma d3e8dfed9c49
Size
705
Isomorphism class hash
d3e8dfed9c49bca09888154b33b5eef1065d026782bb9e87114ab74ff71eefc4
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 20:46:20
Display reorder
660,121,71,146,106,124,72,147,107,122,125,145,70,108,123,126,74,142,109,120,127,75,143,110,118,128,73,144,111,119,129,69,137,104,112,130,67,138,105,113,131,68,136,103,114,132,140,65,100,115,133,141,66,101,116,134,139,64,102,117,135,671,667,669,666,358,218,377,310,374,219,378,311,359,375,376,217,312,360,373,214,380,313,361,370,215,381,314,362,371,216,379,315,363,372,209,383,308,356,365,210,384,309,357,366,208,382,307,355,364,386,212,304,352,368,387,213,305,353,369,385,211,306,354,367,687,685,686,690,583,167,425,509,569,168,426,510,584,570,424,166,508,582,568,170,428,512,586,572,171,429,513,587,573,169,427,511,585,571,165,431,515,589,575,163,432,516,590,576,164,430,514,588,574,434,161,518,592,578,435,162,519,593,579,433,160,517,591,577,672,670,664,668,186,229,401,317,263,230,402,318,184,264,400,231,316,185,262,228,404,320,189,266,226,405,321,187,267,227,403,319,188,265,220,407,323,192,261,221,408,324,190,259,222,406,322,191,260,410,223,326,195,257,411,224,327,193,258,409,225,325,194,256,684,680,675,674,473,269,413,203,389,270,414,204,474,390,412,268,202,472,388,272,416,206,476,392,273,417,207,477,393,271,415,205,475,391,275,419,201,479,395,276,420,199,480,396,274,418,200,478,394,422,278,197,482,398,423,279,198,483,399,421,277,196,481,397,665,662,661,663,449,150,521,557,60,148,522,558,450,58,520,149,556,448,59,153,524,560,452,63,151,525,561,453,61,152,523,559,451,62,156,527,563,455,55,154,528,564,456,56,155,526,562,454,57,530,159,566,458,54,531,157,567,459,52,529,158,565,457,53,694,693,695,696,595,183,581,0,3,181,623,622,620,621,580,182,2,594,1,179,628,629,630,631,180,632,633,634,635,178,625,624,626,627,174,641,640,642,643,172,645,644,646,647,173,637,636,638,639,653,177,652,654,655,657,175,656,658,659,649,176,648,650,651,702,704,701,703,599,80,333,288,598,81,331,286,601,600,332,79,287,596,597,76,329,291,604,605,77,330,289,606,607,78,328,290,602,603,86,339,283,611,610,87,337,284,612,613,85,338,285,609,608,335,82,282,617,616,336,83,280,618,619,334,84,281,615,614,699,700,698,697,497,49,437,545,461,50,438,546,498,462,436,51,544,496,460,48,440,548,500,464,46,441,549,501,465,47,439,547,499,463,40,443,551,503,467,41,444,552,504,468,42,442,550,502,466,446,43,554,506,470,447,44,555,507,471,445,45,553,505,469,679,677,676,683,253,297,341,533,485,295,342,534,254,486,340,296,532,255,484,293,344,536,252,488,294,345,537,250,489,292,343,535,251,487,303,347,539,244,491,301,348,540,245,492,302,346,538,246,490,350,299,542,247,494,351,300,543,248,495,349,298,541,249,493,681,678,673,682,26,37,96,27,238,38,94,22,23,239,95,39,25,24,240,36,99,19,18,241,34,97,21,20,242,35,98,16,17,243,28,91,9,8,236,29,92,4,5,237,30,93,7,6,235,90,31,15,14,232,88,32,10,11,233,89,33,12,13,234,689,688,691,692 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#d368fcffc98defb742f81d5388b25ae4c38c7de7079297526f4ed93fca5d0bec, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 20:46:21 · history