Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma a825c690b7e9…

magma a825c690b7e9
Size
705
Isomorphism class hash
a825c690b7e995acac402d4af58fde25fb523f732c5019ea4287d9e37b16aac9
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 18:20:00
Display reorder
704,93,50,105,81,94,82,48,106,95,83,49,107,80,92,53,104,78,90,51,102,79,91,52,103,72,96,56,84,73,97,54,85,74,98,55,86,99,75,59,87,100,76,57,88,101,77,58,89,63,64,65,62,60,61,69,70,67,68,66,71,683,680,682,681,573,12,585,561,574,562,13,586,575,563,14,587,560,572,15,584,558,570,16,582,559,571,17,583,552,576,18,564,553,577,19,565,554,578,20,566,579,555,21,567,580,556,22,568,581,557,23,569,648,649,650,651,652,653,654,655,658,656,657,659,701,703,700,702,203,448,158,189,201,190,449,156,202,191,447,157,188,199,444,161,186,200,445,159,187,198,446,160,180,164,454,194,181,162,455,192,182,163,453,193,167,183,450,197,165,184,451,195,166,185,452,196,171,172,173,170,168,169,177,178,175,176,174,179,669,671,668,670,378,142,387,363,379,364,143,388,380,365,141,389,362,381,138,386,360,382,139,384,361,383,140,385,369,393,133,376,370,394,134,377,371,395,132,375,392,368,136,372,390,366,137,373,391,367,135,374,348,349,350,351,352,353,354,355,359,357,358,356,679,676,678,677,521,131,531,509,519,507,129,532,520,508,130,533,505,517,127,530,506,518,128,528,504,516,126,529,515,537,122,527,513,538,120,525,514,539,121,526,536,511,125,523,534,512,123,524,535,510,124,522,541,542,540,544,545,543,547,548,549,550,551,546,689,690,688,691,229,638,240,217,230,218,636,241,228,216,637,242,220,232,641,243,221,233,639,244,219,231,640,245,223,246,644,235,224,247,642,236,222,248,643,234,249,226,647,238,250,227,645,239,251,225,646,237,214,215,213,210,211,212,205,206,207,208,209,204,692,694,693,695,503,116,466,489,501,490,114,467,502,491,115,465,488,499,119,462,486,500,117,463,487,498,118,464,480,457,111,494,481,458,112,492,482,456,113,493,460,483,110,497,461,484,108,495,459,485,109,496,479,477,478,475,476,474,470,468,472,473,471,469,661,662,660,663,285,4,298,273,286,274,5,299,287,275,3,297,272,284,1,294,270,282,0,295,271,283,2,296,264,289,10,276,265,290,11,277,266,288,9,278,292,267,6,279,293,268,7,280,291,269,8,281,255,256,257,254,252,253,261,262,259,260,258,263,685,686,684,687,304,40,322,340,305,341,41,323,303,339,39,321,336,300,36,318,337,301,37,319,338,302,38,320,346,313,46,310,347,314,47,311,345,312,45,309,316,342,42,306,317,343,43,307,315,344,44,308,333,334,335,332,330,331,324,325,329,327,328,326,698,697,699,696,438,148,403,427,439,428,149,404,440,426,147,402,430,441,144,406,431,442,145,407,429,443,146,405,425,401,154,436,423,399,155,437,424,400,153,435,397,421,150,432,398,422,151,433,396,420,152,434,409,410,408,412,413,411,415,416,417,418,419,414,666,665,667,664,599,29,600,634,597,635,27,601,598,633,28,602,630,595,25,603,631,596,26,604,632,594,24,605,625,606,35,590,626,607,33,588,624,608,34,589,609,628,31,593,610,629,32,591,611,627,30,592,618,619,620,621,622,623,616,617,614,612,613,615,674,673,675,672 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#7b4d86832894383b0b7ce3dfc16e526670032b07fced110816f25e14f2157e1a, 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 18:20:01 · history