Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 432b3db3ca3e…

magma 432b3db3ca3e
Size
705
Isomorphism class hash
432b3db3ca3ec1345df60c88678532ae8227835ecf13327448d1fc60a130539d
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 17:23:20
Display reorder
660,285,292,51,582,274,283,293,580,49,275,581,294,284,50,276,281,295,585,54,277,282,296,583,52,278,280,297,584,53,279,298,291,588,46,272,299,289,586,47,273,300,290,587,48,271,287,301,591,45,268,288,302,589,43,269,286,303,590,44,270,687,688,686,685,361,373,329,84,349,362,374,82,330,350,83,375,363,328,351,360,372,80,332,348,358,370,81,333,346,359,371,79,331,347,364,352,90,335,340,365,353,88,336,341,366,354,89,334,342,355,367,86,338,343,356,368,87,339,344,357,369,85,337,345,703,704,701,702,558,571,538,256,549,556,572,257,539,547,258,573,557,540,548,561,570,259,541,545,559,568,260,542,546,560,569,261,543,544,577,564,262,536,555,578,562,263,537,553,579,563,264,535,554,567,576,265,532,551,565,574,266,533,552,566,575,267,534,550,671,672,670,669,385,399,411,210,423,386,397,208,409,421,209,398,387,410,422,384,395,206,407,419,382,396,207,408,420,383,394,205,406,418,390,376,201,402,414,388,377,199,400,412,389,378,200,401,413,379,393,204,405,417,380,391,202,403,415,381,392,203,404,416,679,680,678,677,445,459,471,179,433,446,457,180,469,434,178,458,447,470,435,444,455,175,467,432,442,456,176,468,430,443,454,177,466,431,450,436,185,462,424,448,437,186,460,425,449,438,184,461,426,439,453,181,465,427,440,451,182,463,428,441,452,183,464,429,692,691,690,689,17,516,3,61,229,15,514,62,4,230,63,515,16,5,231,13,519,64,2,232,14,517,65,1,233,12,518,66,0,234,511,23,59,9,227,512,21,60,10,228,513,22,58,11,226,19,510,55,8,223,20,508,56,6,224,18,509,57,7,225,699,700,698,697,130,142,154,117,168,131,143,115,155,166,116,144,132,156,167,129,141,120,153,164,127,139,118,151,165,128,140,119,152,163,148,136,123,160,174,149,137,121,161,172,150,138,122,162,173,135,147,126,159,170,133,145,124,157,171,134,146,125,158,169,663,664,662,661,621,630,600,306,606,619,628,304,598,604,305,629,620,599,605,617,633,309,603,609,618,631,307,601,607,616,632,308,602,608,636,627,312,595,612,634,625,310,596,610,635,626,311,597,611,623,639,315,594,615,624,637,313,592,613,622,638,314,593,614,682,683,684,681,653,655,652,527,654,657,659,528,656,658,526,651,648,649,650,24,249,530,248,247,641,642,531,640,643,646,647,529,645,644,254,25,525,239,242,255,26,523,240,243,253,27,524,238,241,28,250,521,235,245,29,251,522,236,246,30,252,520,237,244,695,696,693,694,193,479,486,213,499,194,480,211,484,500,212,478,195,485,501,196,482,216,489,498,197,483,214,487,496,198,481,215,488,497,477,191,219,492,505,475,192,217,490,506,476,190,218,491,507,187,473,222,495,504,188,474,220,493,502,189,472,221,494,503,667,668,665,666,97,106,324,32,67,98,107,33,322,68,31,108,99,323,69,100,105,35,327,70,101,103,36,325,71,102,104,34,326,72,112,95,38,319,73,113,96,39,320,74,114,94,37,321,75,91,111,41,318,76,92,109,42,316,77,93,110,40,317,78,675,676,673,674 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#51b008b28ab03bd312921cf92cf8265fda62df0fbe14e18f3974b5c43c79b0a4, 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 17:23:21 · history