Equation 677 Database

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Magma 0b982cb14b59…

magma 0b982cb14b59
Size
705
Isomorphism class hash
0b982cb14b5988a0d3c8bd96aca53c4245bd8dc167a3b423168dabafd1df09a4
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 18:06:27
Display reorder
660,375,251,329,271,333,376,334,252,330,269,253,332,374,331,270,378,250,336,328,267,379,248,337,326,268,377,249,335,327,266,339,257,373,320,262,340,258,371,321,260,338,259,372,322,261,256,342,369,323,265,254,343,370,324,263,255,341,368,325,264,661,671,662,667,46,498,134,318,144,44,145,499,132,319,497,146,45,133,317,42,494,143,130,314,43,495,141,131,315,41,496,142,129,316,150,489,37,140,309,151,490,35,138,310,152,488,36,139,308,492,149,40,136,312,493,147,38,137,313,491,148,39,135,311,690,687,686,685,167,414,235,364,641,165,642,415,233,362,413,640,166,234,363,170,410,637,231,367,168,411,638,232,365,169,412,639,230,366,632,405,173,226,359,633,406,171,224,360,631,404,172,225,361,408,635,176,229,358,409,636,174,227,356,407,634,175,228,357,669,663,664,672,2,158,510,438,534,1,535,156,511,439,157,533,0,509,437,5,154,530,506,434,3,155,531,507,435,4,153,532,508,436,525,164,8,501,429,526,162,6,502,430,524,163,7,500,428,160,528,11,504,432,161,529,9,505,433,159,527,10,503,431,679,682,676,680,82,593,546,617,522,83,523,594,547,618,592,521,81,545,616,85,589,518,542,613,86,590,519,543,614,84,591,520,544,615,513,584,88,537,608,514,585,89,538,609,512,583,87,536,607,587,516,91,540,611,588,517,92,541,612,586,515,90,539,610,666,668,670,665,352,462,75,581,219,350,220,463,76,582,461,218,351,77,580,355,458,222,78,577,353,459,223,79,578,354,460,221,80,579,217,453,347,73,572,215,454,348,74,573,216,452,349,72,571,456,213,346,69,575,457,214,344,70,576,455,212,345,71,574,693,694,696,697,200,65,189,570,653,201,659,658,657,656,64,652,202,190,569,203,68,649,192,566,204,66,650,193,567,205,67,651,191,568,644,63,206,195,561,645,61,207,196,562,643,62,208,194,560,59,647,209,198,564,60,648,210,199,565,58,646,211,197,563,703,702,701,704,287,24,47,474,100,288,101,654,655,475,25,99,289,48,473,286,27,103,49,470,284,28,104,50,471,285,26,102,51,472,98,30,293,56,465,96,31,294,57,466,97,29,295,55,464,33,94,292,52,468,34,95,290,53,469,32,93,291,54,467,699,700,695,698,128,426,402,380,450,126,451,427,403,381,425,449,127,401,382,124,422,446,398,383,125,423,447,399,384,123,424,448,400,385,441,417,119,393,386,442,418,117,394,387,440,416,118,392,388,420,444,122,396,389,421,445,120,397,390,419,443,121,395,391,674,675,683,677,304,558,629,486,20,302,18,559,630,487,557,19,303,628,485,307,554,23,625,482,305,555,21,626,483,306,556,22,627,484,15,549,299,620,477,16,550,300,621,478,17,548,301,619,476,552,14,298,623,480,553,12,296,624,481,551,13,297,622,479,684,681,678,673,181,605,115,243,278,182,279,606,116,244,604,280,180,114,242,177,601,281,111,246,178,602,282,112,247,179,603,283,113,245,276,596,187,106,241,277,597,188,107,239,275,595,186,105,240,599,272,183,109,237,600,273,184,110,238,598,274,185,108,236,688,689,692,691 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#62d5cd0053185ccae094f96e2ae535daccc2dacd55a9f14470e4ff2a7e2e534c, 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 18:06:29 · history