Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma e48e2cd0099a…

magma e48e2cd0099a
Size
705
Isomorphism class hash
e48e2cd0099add10945111fac142a6e8a5675a40dcb2f77e600a86dd5b545fa3
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 16:46:53
Display reorder
660,136,135,137,134,132,133,141,142,143,140,138,139,94,170,168,95,169,93,173,90,171,91,172,92,176,85,174,86,175,84,179,88,177,89,178,87,314,398,312,396,313,397,317,401,315,399,316,400,320,404,318,402,319,403,323,407,321,405,322,406,661,669,663,677,43,42,44,45,46,47,40,41,39,36,37,38,34,549,550,35,551,33,548,30,546,31,547,32,540,25,541,26,542,24,543,28,544,29,545,27,609,477,610,478,611,479,608,476,606,474,607,475,600,468,601,469,602,470,603,471,604,472,605,473,682,689,686,696,430,429,431,428,426,427,420,421,422,423,424,425,161,280,281,159,279,160,276,157,277,158,278,156,286,167,287,165,285,166,282,163,283,164,284,162,362,350,360,348,361,349,365,353,363,351,364,352,368,356,366,354,367,355,371,359,369,357,370,358,666,668,665,673,497,496,495,492,493,494,502,503,501,498,499,500,480,612,613,481,614,482,615,483,616,484,617,485,618,486,619,487,620,488,621,489,622,490,623,491,560,8,558,6,559,7,563,11,561,9,562,10,555,3,556,4,557,5,554,2,552,1,553,0,670,680,676,687,209,208,207,204,205,206,214,215,213,210,211,212,624,572,570,625,571,626,575,627,573,628,574,629,567,630,568,631,569,632,566,633,564,634,565,635,513,201,514,202,515,203,512,200,510,198,511,199,504,192,505,193,506,194,507,195,508,196,509,197,664,667,662,678,155,154,153,150,151,152,145,146,144,148,149,147,342,273,274,343,275,344,272,345,270,346,271,347,264,340,265,341,266,339,267,336,268,337,269,338,331,415,332,416,330,414,334,418,335,419,333,417,329,413,327,411,328,412,325,409,326,410,324,408,691,698,694,701,18,20,19,23,21,22,15,16,17,14,12,13,229,258,259,230,260,228,261,232,262,233,263,231,256,235,257,236,255,234,252,238,253,239,254,237,240,219,241,220,242,221,243,218,244,216,245,217,246,225,247,226,248,227,249,224,250,222,251,223,699,703,702,704,586,585,587,584,582,583,576,577,578,579,580,581,519,50,48,520,49,521,53,518,51,516,52,517,56,525,54,526,55,527,59,524,57,522,58,523,184,645,185,646,183,647,180,644,181,642,182,643,190,636,191,637,189,638,186,639,187,640,188,641,693,697,695,700,389,388,387,384,385,386,394,395,393,390,391,392,74,122,120,72,121,73,125,77,123,75,124,76,128,80,126,78,127,79,131,83,129,81,130,82,449,300,447,301,448,302,445,303,446,304,444,305,455,306,453,307,454,308,451,309,452,310,450,311,671,681,675,684,65,64,63,60,61,62,70,71,69,66,67,68,458,533,531,456,532,457,529,461,530,459,528,460,539,464,537,462,538,463,535,467,536,465,534,466,648,593,649,591,650,592,651,589,652,590,653,588,654,599,655,597,656,598,657,595,658,596,659,594,672,679,674,685,116,115,114,118,119,117,113,111,112,109,110,108,293,378,379,291,380,292,381,289,382,290,383,288,376,299,377,297,375,298,372,295,373,296,374,294,98,439,96,440,97,438,101,442,99,443,100,441,104,437,102,435,103,436,107,433,105,434,106,432,683,690,688,692 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#3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d, M = {62} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 16:46:54 · history