Equation 677 Database

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Magma c7211e64dc7e…

magma c7211e64dc7e
Size
705
Isomorphism class hash
c7211e64dc7e401f8f5ca199e2a8f8d4ff80d43460b061c3ebb1d45cd516aeea
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 17:23:55
Display reorder
660,357,298,499,130,405,358,296,131,500,406,129,297,356,498,404,353,294,126,495,401,354,295,127,496,402,355,293,128,497,403,289,348,121,490,396,287,349,122,491,397,288,347,120,489,395,351,292,124,493,399,352,290,125,494,400,350,291,123,492,398,661,666,663,669,228,249,417,100,220,229,250,101,418,218,99,248,227,416,219,231,245,96,413,216,232,246,97,414,217,230,247,98,415,215,240,234,106,408,226,241,235,107,409,224,239,233,105,407,225,237,243,102,411,222,238,244,103,412,223,236,242,104,410,221,686,687,688,685,523,571,463,318,12,524,572,319,464,13,317,570,522,462,14,519,567,321,459,15,520,568,322,460,16,521,569,320,461,17,562,514,316,454,18,563,515,314,455,19,561,513,315,453,20,517,565,312,457,21,518,566,313,458,22,516,564,311,456,23,667,664,672,670,185,607,32,260,487,186,608,261,30,488,262,606,187,31,486,188,603,259,35,483,189,604,257,33,484,190,605,258,34,485,598,183,251,27,478,599,184,252,28,479,597,182,253,29,477,179,601,254,26,481,180,602,255,24,482,181,600,256,25,480,673,680,676,682,547,201,49,44,595,548,202,42,50,596,43,200,546,48,594,543,197,47,52,591,544,198,45,53,592,545,199,46,51,593,192,538,39,55,586,193,539,40,56,587,191,537,41,54,585,541,195,38,58,589,542,196,36,59,590,540,194,37,57,588,668,665,671,662,133,155,75,301,535,134,153,299,76,536,300,154,132,77,534,136,151,304,74,531,137,152,302,72,532,135,150,303,73,533,146,139,307,81,526,144,140,305,82,527,145,138,306,83,525,142,149,310,80,529,143,147,308,78,530,141,148,309,79,528,696,693,694,698,631,172,419,158,440,659,658,156,657,656,157,171,630,420,439,627,168,161,422,436,628,169,159,423,437,629,170,160,421,438,178,622,164,425,431,176,623,162,426,432,177,621,163,424,430,625,174,167,428,434,626,175,165,429,435,624,173,166,427,433,704,703,701,702,619,205,653,66,652,620,203,67,655,654,68,204,618,650,651,615,208,69,644,645,616,206,70,647,646,617,207,71,649,648,211,610,64,635,634,209,611,65,637,636,210,609,63,633,632,613,214,60,640,641,614,212,61,643,642,612,213,62,638,639,697,699,700,695,341,108,583,394,475,342,109,392,584,476,393,110,343,582,474,344,111,390,579,471,345,112,391,580,472,346,113,389,581,473,114,339,385,574,466,115,340,383,575,467,116,338,384,573,465,335,117,388,577,469,336,118,386,578,470,337,119,387,576,468,683,681,675,684,559,84,511,285,451,560,85,286,512,452,284,86,558,510,450,555,87,281,507,447,556,88,282,508,448,557,89,283,509,449,90,550,276,502,442,91,551,277,503,443,92,549,275,501,441,553,93,279,505,445,554,94,280,506,446,552,95,278,504,444,679,678,674,677,375,2,269,325,362,376,1,323,270,363,324,0,374,271,364,371,5,328,272,361,372,3,326,273,359,373,4,327,274,360,8,381,331,267,368,6,382,329,268,369,7,380,330,266,370,377,11,334,263,367,378,9,332,264,365,379,10,333,265,366,689,692,691,690 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#51b008b28ab03bd312921cf92cf8265fda62df0fbe14e18f3974b5c43c79b0a4, 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 17:23:56 · history