Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma c496100dc237…

magma c496100dc237
Size
705
Isomorphism class hash
c496100dc2376ecb4bf130609c88675caee92d6fb670caa16e62232f3792b1a2
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 17:29:21
Display reorder
660,75,244,600,269,256,73,245,270,257,598,74,246,599,268,258,247,78,603,272,259,248,76,601,273,260,249,77,602,271,261,81,250,595,275,262,79,251,596,276,263,80,252,597,274,264,84,253,594,278,265,82,254,592,279,266,83,255,593,277,267,687,688,686,685,317,378,364,352,340,318,376,353,341,365,316,377,366,354,342,381,320,367,355,343,379,321,368,356,344,380,319,369,357,345,323,384,370,358,346,324,382,371,359,347,322,383,372,360,348,326,387,373,361,349,327,385,374,362,350,325,386,375,363,351,703,704,701,702,239,571,558,544,591,240,572,545,589,556,238,573,557,546,590,570,242,561,547,587,568,243,559,548,588,569,241,560,549,586,237,577,564,550,582,235,578,562,551,580,236,579,563,552,581,233,576,567,553,585,234,574,565,554,583,232,575,566,555,584,671,672,670,669,14,403,396,424,422,15,404,425,423,394,13,405,395,426,421,402,17,399,427,418,400,18,397,428,419,401,16,398,429,420,20,409,391,430,413,21,410,392,431,414,19,411,393,432,412,23,408,390,433,416,24,406,388,434,417,22,407,389,435,415,679,680,678,677,441,104,133,121,109,439,105,122,110,134,440,103,135,123,111,107,437,136,124,112,108,438,137,125,113,106,436,138,126,114,447,102,139,127,115,445,100,140,128,116,446,101,141,129,117,443,98,142,130,118,444,99,143,131,119,442,97,144,132,120,692,691,690,689,63,503,160,520,508,61,504,521,509,161,62,502,162,522,510,506,66,159,523,511,507,64,157,524,512,505,65,158,525,513,69,501,166,526,514,67,499,167,527,515,68,500,168,528,516,72,497,165,529,517,70,498,163,530,518,71,496,164,531,519,699,700,698,697,28,43,91,6,38,33,46,4,40,92,27,50,93,5,35,52,39,94,2,25,55,42,95,3,30,59,36,96,0,32,48,37,89,12,56,51,41,90,10,58,45,34,88,11,53,57,26,85,8,44,60,29,86,9,47,54,31,87,7,49,663,664,662,661,281,642,628,616,604,282,640,617,605,629,280,641,630,618,606,645,284,631,619,607,643,285,632,620,608,644,283,633,621,609,287,648,634,622,610,288,646,635,623,611,286,647,636,624,612,290,651,637,625,613,291,649,638,626,614,289,650,639,627,615,682,683,684,681,536,177,190,224,186,537,175,225,187,191,535,176,189,223,185,188,532,1,222,184,652,533,653,654,655,657,534,658,659,656,542,172,196,230,179,543,173,197,231,180,541,174,195,229,178,538,171,192,226,182,539,169,193,227,183,540,170,194,228,181,695,696,693,694,155,474,470,459,487,156,472,457,488,471,154,473,469,458,489,477,151,466,455,486,475,152,467,456,484,476,153,468,454,485,146,480,461,450,493,147,478,462,448,494,145,479,460,449,495,149,483,464,453,492,150,481,465,451,490,148,482,463,452,491,667,668,665,666,330,199,309,300,215,328,200,298,213,307,329,198,308,299,214,202,333,305,303,211,203,331,306,301,212,201,332,304,302,210,336,205,315,295,221,334,206,313,296,219,335,204,314,297,220,339,208,311,294,217,337,209,312,292,218,338,207,310,293,216,675,676,673,674 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#58222ccd0574e7adf03b9b32a848bfc3e464df8d7127a3e76f96a819fe65341a, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 17:29:24 · history