Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma e7fd82319bd8…

magma e7fd82319bd8
Size
705
Isomorphism class hash
e7fd82319bd83875dd269bb36505a69c0d01730982d268b2027cbb105abc8f07
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 15:56:37
Display reorder
660,328,131,143,320,118,329,132,321,144,119,330,130,142,319,120,127,327,139,323,117,128,325,140,324,115,129,326,141,322,116,122,318,334,134,109,123,316,335,135,110,121,317,336,133,111,314,125,333,137,112,315,126,331,138,113,313,124,332,136,114,685,686,688,687,68,177,407,183,76,69,175,181,408,77,67,176,406,182,78,180,71,403,186,75,178,72,404,184,73,179,70,405,185,74,172,189,66,398,82,173,187,64,399,83,174,188,65,397,84,192,171,62,401,81,190,169,63,402,79,191,170,61,400,80,701,702,704,703,293,273,586,279,310,294,271,277,584,311,292,272,585,278,312,276,289,589,282,309,274,290,587,280,307,275,291,588,281,308,268,285,299,592,301,269,283,300,590,302,270,284,298,591,303,288,267,295,595,304,286,265,296,593,305,287,266,297,594,306,670,669,672,671,432,445,200,413,434,430,446,414,201,435,431,447,199,412,433,448,428,203,409,437,449,429,204,410,438,450,427,202,411,436,451,419,423,198,440,452,420,421,196,441,453,418,422,197,439,415,454,426,194,443,416,455,424,195,444,417,456,425,193,442,680,677,679,678,473,504,18,457,490,474,502,458,19,491,472,503,20,459,492,500,469,21,460,489,501,470,22,461,487,499,471,23,462,488,495,463,479,16,481,493,464,480,17,482,494,465,478,15,483,466,498,475,12,484,467,496,476,13,485,468,497,477,14,486,689,690,691,692,529,32,108,525,249,530,30,523,106,247,531,31,107,524,248,35,532,104,528,252,33,533,105,526,250,34,534,103,527,251,27,520,535,99,244,28,521,536,97,245,29,522,537,98,246,519,26,538,102,243,517,24,539,100,241,518,25,540,101,242,697,698,700,699,636,619,655,622,606,637,617,620,653,607,635,618,654,621,605,615,632,651,625,602,616,633,652,623,603,614,634,650,624,604,610,628,642,646,597,608,626,643,644,598,609,627,641,645,596,631,613,638,649,600,629,611,639,647,601,630,612,640,648,599,661,662,664,663,49,343,6,152,44,50,344,153,7,42,48,345,8,151,43,346,52,9,155,47,347,53,10,156,45,348,51,11,154,46,341,150,55,4,39,342,148,56,5,40,340,149,54,3,41,146,337,58,1,38,147,338,59,0,36,145,339,57,2,37,682,681,684,683,562,544,261,561,576,563,545,559,259,577,564,546,260,560,578,543,565,264,557,575,541,566,262,558,573,542,567,263,556,574,550,552,568,256,582,551,60,569,257,583,656,657,658,258,659,555,549,570,255,581,553,547,571,253,579,554,548,572,254,580,693,694,696,695,231,214,87,228,513,229,215,226,85,511,230,216,86,227,512,213,234,90,224,516,211,232,88,225,514,212,233,89,223,515,205,219,237,93,508,206,217,235,91,509,207,218,236,92,510,222,208,240,96,507,220,209,238,94,505,221,210,239,95,506,666,665,668,667,353,375,160,388,372,354,373,389,161,370,352,374,162,390,371,378,349,159,387,368,376,350,157,385,369,377,351,158,386,367,381,394,359,166,363,379,395,360,167,361,380,396,358,168,362,393,384,355,165,366,391,382,356,163,364,392,383,357,164,365,674,673,676,675 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#25532901b7174194dca0f8f453aa2ae473cc5b2aa34d04b35f0c3beb206af29c, 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 15:56:38 · history