Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 5a1f468cd81b…

magma 5a1f468cd81b
Size
705
Isomorphism class hash
5a1f468cd81ba2c835e0be2b6360215f08de848896c019832e197096dbb05e10
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 17:26:13
Display reorder
660,568,580,556,544,87,569,581,85,557,545,570,582,86,558,546,571,583,90,559,547,572,584,88,560,548,573,585,89,561,549,562,586,574,93,550,587,575,91,563,551,588,576,92,564,552,577,589,96,565,553,578,590,94,566,554,579,591,95,567,555,687,688,686,685,320,334,362,251,387,321,332,388,363,252,322,333,386,364,253,323,337,390,365,250,324,335,391,366,248,325,336,389,367,249,360,340,326,385,257,338,327,383,361,258,339,328,384,359,259,329,343,381,356,256,330,341,382,357,254,331,342,380,358,255,703,704,701,702,522,535,508,496,81,520,536,79,509,497,521,537,80,510,498,525,534,84,511,499,523,532,82,512,500,524,533,83,513,501,514,541,528,76,502,542,526,77,515,503,543,527,78,516,504,531,540,75,517,505,529,538,73,518,506,530,539,74,519,507,671,672,670,669,143,51,194,8,396,144,49,397,195,9,142,50,395,196,7,139,54,392,197,11,140,52,393,198,12,141,53,394,199,10,192,57,134,402,6,55,135,403,193,4,56,133,401,191,5,137,60,398,188,2,138,58,399,189,3,136,59,400,190,0,679,680,678,677,212,224,200,236,406,213,225,404,201,237,214,226,405,202,238,215,227,409,203,239,216,228,407,204,240,217,229,408,205,241,206,230,218,412,242,231,219,410,207,243,232,220,411,208,244,221,233,415,209,245,222,234,413,210,246,223,235,414,211,247,692,691,690,689,169,278,157,470,145,170,279,146,158,471,171,280,147,159,472,172,281,148,160,473,173,282,149,161,474,174,283,150,162,475,163,276,175,151,468,277,176,152,164,469,275,177,153,165,467,178,272,154,166,464,179,273,155,167,465,180,274,156,168,466,699,700,698,697,42,26,119,103,22,40,27,23,120,104,41,25,24,118,105,38,29,21,115,106,39,30,19,116,107,37,28,20,117,108,110,32,48,13,101,33,46,14,111,102,31,47,15,109,100,44,35,16,113,97,45,36,17,114,98,43,34,18,112,99,663,664,662,661,616,630,604,592,285,617,628,286,605,593,618,629,284,606,594,619,633,288,607,595,620,631,289,608,596,621,632,287,609,597,610,636,622,291,598,634,623,292,611,599,635,624,290,612,600,625,639,294,613,601,626,637,295,614,602,627,638,293,615,603,682,683,684,681,653,655,654,652,131,657,659,132,658,656,648,651,130,650,649,1,489,127,482,181,641,642,128,640,643,644,647,129,646,645,481,494,484,122,185,495,485,123,479,186,493,483,121,480,187,487,490,125,477,184,488,491,126,478,182,486,492,124,476,183,695,696,693,694,442,456,433,418,63,440,457,61,431,416,441,455,62,432,417,445,452,66,429,421,443,453,64,430,419,444,454,65,428,420,439,462,448,69,424,463,446,67,437,422,461,447,68,438,423,451,458,72,435,427,449,459,70,436,425,450,460,71,434,426,667,668,665,666,313,374,299,346,261,311,375,262,300,344,312,376,260,301,345,309,377,264,298,349,310,378,265,296,347,308,379,263,297,348,305,372,319,267,352,373,317,268,306,350,371,318,266,307,351,315,368,270,304,355,316,369,271,302,353,314,370,269,303,354,675,676,673,674 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#5751a2f21b762bdcbb8d7ca8109ff664440cd913db63bda4230c3be52dd8f5e2, 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 17:26:13 · history