Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 59839e6011ae…

magma 59839e6011ae
Size
705
Isomorphism class hash
59839e6011aebbe35283ab12668157d5717875f0348bf6ff23274f2842ce3f5e
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 15:08:12
Display reorder
660,323,165,342,554,514,324,166,343,555,515,325,341,553,513,164,168,322,338,550,510,169,320,339,551,511,167,321,340,552,512,329,171,333,545,505,330,172,334,546,506,331,170,332,544,504,548,174,328,336,508,175,326,337,549,509,173,327,335,547,507,683,685,676,687,242,289,454,69,220,243,287,455,70,218,244,453,68,219,288,285,245,450,72,223,286,246,451,73,221,284,247,452,71,222,240,295,445,75,215,241,293,446,76,216,239,294,444,74,217,78,291,236,448,214,292,237,449,79,212,290,238,447,77,213,669,670,665,661,466,80,306,255,490,467,81,307,256,491,465,305,254,489,82,83,462,302,258,486,84,463,303,259,487,85,464,304,257,488,457,86,297,253,481,458,87,298,251,482,456,88,296,252,480,249,89,460,300,484,90,461,301,250,485,91,459,299,248,483,682,674,675,681,649,41,644,646,650,657,42,653,654,658,641,636,638,642,40,44,617,612,614,618,45,625,620,622,626,43,633,629,630,634,441,47,18,39,517,442,48,19,37,518,440,46,17,38,516,597,50,599,600,601,51,609,605,607,610,49,443,16,20,519,704,697,703,699,179,148,114,414,318,180,146,115,415,319,181,113,413,317,147,151,178,110,410,314,149,176,111,411,315,150,177,112,412,316,185,143,105,405,309,186,144,106,406,310,187,145,104,404,308,408,142,184,108,312,140,182,109,409,313,141,183,107,407,311,690,691,693,689,438,129,261,478,502,439,130,262,479,503,437,260,477,501,128,132,434,264,474,498,133,435,265,475,499,131,436,263,476,500,429,135,267,469,493,430,136,268,470,494,428,134,266,468,492,472,138,432,270,496,139,433,271,473,497,137,431,269,471,495,667,666,672,664,192,55,29,582,8,193,56,27,583,6,191,28,581,7,57,54,188,32,578,11,52,189,30,579,9,53,190,31,580,10,198,61,24,573,3,199,62,25,574,4,197,63,26,572,5,576,60,194,23,2,58,195,21,577,1,59,196,22,575,0,695,694,696,692,566,121,354,594,542,567,119,355,595,543,565,353,593,541,120,117,562,350,590,538,118,563,351,591,539,116,564,352,592,540,557,127,345,585,533,558,125,346,586,534,556,126,344,584,532,588,123,560,348,536,124,561,349,589,537,122,559,347,587,535,684,688,677,686,651,203,648,645,647,659,204,656,652,655,643,640,637,639,205,202,619,616,613,615,200,627,624,621,623,201,635,632,628,631,569,209,65,15,35,570,210,66,13,33,568,211,67,14,34,602,208,603,598,596,206,611,608,604,606,207,571,64,12,36,702,700,698,701,378,235,97,530,402,379,233,95,531,403,377,96,529,401,234,231,374,93,526,398,232,375,94,527,399,230,376,92,528,400,369,226,103,521,393,370,224,101,522,394,368,225,102,520,392,524,229,372,99,396,227,373,100,525,397,228,371,98,523,395,663,668,671,662,426,160,282,366,390,427,158,283,367,391,425,281,365,389,159,163,422,278,362,386,161,423,279,363,387,162,424,280,364,388,417,155,273,357,381,418,156,274,358,382,416,157,272,356,380,360,154,420,276,384,152,421,277,361,385,153,419,275,359,383,679,678,673,680 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#055eb219830141adc126b0e3c095dec26895b5c9338d223a671ccb522fe00e95, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 15:08:14 · history