Equation 677 Database

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Magma 6acb07fe014d…

magma 6acb07fe014d
Size
595
Isomorphism class hash
6acb07fe014d53847db40a82d9241842b592682b4ffbfaa852c5309fcf613c9b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 16:51:50
Display reorder
59,64,60,61,62,63,94,93,95,96,91,92,118,117,113,114,115,116,426,428,427,429,430,431,287,286,285,283,284,282,523,541,575,570,577,240,239,172,236,237,238,167,131,132,133,134,135,109,108,104,105,106,107,126,125,127,211,212,163,190,189,191,155,65,66,142,141,143,140,144,244,173,245,241,242,243,174,177,176,175,150,178,179,437,436,435,433,434,432,440,438,439,442,443,441,451,452,450,453,454,455,486,488,487,491,489,490,421,420,422,423,424,425,495,494,496,497,498,499,384,386,385,389,387,388,263,262,261,260,259,258,549,550,521,520,514,516,510,522,572,562,580,586,552,593,553,592,31,30,32,33,34,35,86,87,88,89,84,85,2,1,3,4,5,0,72,71,67,68,69,70,43,42,44,45,46,47,55,54,56,57,58,188,213,165,214,215,216,164,224,223,168,220,221,222,353,352,351,349,350,348,492,493,504,502,503,505,500,506,501,508,507,509,484,483,485,481,480,482,444,445,446,447,448,449,479,478,477,474,476,475,276,278,277,281,279,280,471,473,472,469,468,470,534,535,518,551,548,512,532,513,557,563,564,567,582,581,588,559,49,48,50,51,52,53,23,18,19,20,21,22,25,24,26,27,28,29,13,12,14,15,16,17,78,77,73,74,75,76,146,145,147,148,149,257,253,246,254,255,256,219,248,249,247,250,251,252,300,302,301,305,303,304,270,272,271,275,273,274,418,417,419,415,416,414,293,292,291,289,290,288,306,308,307,311,309,310,365,364,363,361,362,360,411,413,412,410,408,409,394,393,395,391,392,390,543,538,515,527,526,525,524,511,556,565,554,555,587,594,590,560,40,39,41,36,37,38,83,195,196,197,156,194,185,153,186,154,187,184,218,217,166,128,129,130,137,136,138,139,230,231,171,234,235,232,170,233,152,180,181,182,183,151,228,227,229,169,225,226,457,461,460,456,459,458,359,358,357,355,356,354,404,403,402,407,405,406,325,324,326,327,328,329,265,264,266,267,268,269,298,297,299,294,295,296,346,345,347,342,343,344,396,398,397,399,400,401,545,547,537,531,530,528,542,519,558,591,585,566,568,573,589,561,6,11,7,8,9,10,90,201,198,157,199,200,203,159,204,205,158,202,210,209,162,111,112,110,82,81,79,80,192,193,206,207,160,208,161,97,102,101,103,98,99,100,122,121,123,124,119,120,462,463,467,464,466,465,382,381,383,378,379,380,318,320,319,321,322,323,334,333,335,330,331,332,371,370,369,367,368,366,314,313,312,316,317,315,374,373,372,376,377,375,341,340,339,338,336,337,533,536,517,546,544,529,539,540,574,584,583,576,571,569,579,578 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#5ad34b2f8758383b4965947b4701d5813e2a88f030dcc851453e9c1dba339352, M = the submagma generated by {12, 18} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 16:51:51 · history