Equation 677 Database

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Magma 519b30da8b7e…

magma 519b30da8b7e
Size
399
Isomorphism class hash
519b30da8b7e4f9bf08c0298bd5a55a6ec96e80ab668e73aec97e3157a1886b1
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 13:18:47
Display reorder
308,309,310,311,312,313,314,306,307,317,318,319,320,321,322,323,315,316,380,327,270,292,218,328,219,271,293,329,220,272,294,330,221,273,295,331,222,274,296,332,223,275,288,324,224,276,289,325,216,277,290,326,217,278,291,227,336,279,301,228,337,280,302,229,338,281,303,230,339,282,304,231,340,283,305,232,341,284,297,233,333,285,298,225,334,286,299,226,335,287,300,391,385,386,392,259,101,202,132,260,133,102,203,252,134,103,204,253,126,104,205,254,127,105,206,255,128,106,198,256,129,107,199,257,130,99,200,258,131,100,201,141,268,94,211,142,269,95,212,143,261,96,213,135,262,97,214,136,263,98,215,137,264,90,207,138,265,91,208,139,266,92,209,140,267,93,210,383,389,390,384,82,145,41,115,83,116,146,42,84,108,147,43,85,109,148,44,86,110,149,36,87,111,150,37,88,112,151,38,89,113,152,39,81,114,144,40,124,75,154,50,125,76,155,51,117,77,156,52,118,78,157,53,119,79,158,45,120,80,159,46,121,72,160,47,122,73,161,48,123,74,153,49,388,398,397,387,348,244,342,183,350,184,245,344,352,185,246,346,354,186,247,349,356,187,248,351,358,188,249,353,343,180,250,355,345,181,251,357,347,182,243,359,192,367,237,360,193,369,238,362,194,371,239,364,195,373,240,366,196,375,241,368,197,377,242,370,189,361,234,372,190,363,235,374,191,365,236,376,394,395,396,393,3,163,23,71,4,63,164,24,5,64,165,25,6,65,166,26,7,66,167,18,8,67,168,19,1,68,169,20,0,69,170,21,2,70,162,22,55,12,172,32,56,13,173,33,57,14,174,34,58,15,175,35,59,16,176,27,60,17,177,28,61,9,178,29,62,10,179,30,54,11,171,31,378,381,379,382 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#a6f23f6eecd78957cff8bdba49faaa095bb9aea749a152f146f2ef0ad1d22f67, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-07 13:18:49 · history