Equation 677 Database

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Magma be51c30affb0…

magma be51c30affb0
Size
381
Isomorphism class hash
be51c30affb0c5be3d487d9e106c1f394a2f8bd3d618a8631973bc0e31997fad
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:41:07
Display reorder
380,16,15,17,12,13,14,279,284,289,294,299,274,35,30,31,32,33,34,264,269,244,249,254,259,27,28,29,24,25,26,1,0,2,3,4,5,23,18,19,20,21,22,300,302,303,304,305,301,53,48,49,50,51,52,7,8,9,10,11,6,59,55,56,58,57,54,334,340,379,335,339,331,333,332,373,336,151,150,152,153,148,149,278,283,288,293,298,273,237,86,87,88,85,84,263,268,243,248,253,258,93,94,89,90,91,92,158,159,154,155,156,157,142,143,144,145,146,147,324,325,326,327,328,329,198,199,200,195,196,197,164,165,160,161,162,163,190,192,193,189,194,191,353,361,378,344,362,356,354,355,372,345,72,77,73,74,75,76,277,282,287,292,297,272,45,46,47,42,43,44,262,267,242,247,252,257,38,39,40,41,36,37,133,134,135,130,131,132,78,79,80,81,82,83,318,319,320,321,322,323,233,234,235,236,231,232,141,136,137,138,139,140,227,229,230,226,225,228,342,367,375,338,368,352,343,351,371,337,173,239,174,175,176,172,276,281,286,290,295,271,121,122,123,118,119,120,261,266,240,246,251,256,127,128,129,124,125,126,98,99,100,95,96,97,167,168,169,170,171,166,309,310,311,306,307,308,203,204,205,206,201,202,106,101,102,103,104,105,208,210,211,207,212,209,357,364,377,350,363,347,358,346,370,369,218,217,213,214,215,216,275,280,285,291,296,270,115,116,117,112,113,114,260,265,241,245,250,255,109,238,110,111,107,108,66,67,68,69,70,71,223,224,219,220,221,222,313,314,315,316,317,312,182,177,178,179,180,181,64,65,60,61,62,63,188,184,185,187,186,183,366,360,376,349,359,330,365,341,374,348 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#b66edbbdcc18ab822aeb8c0e517cc0500614bfcd68d760a94b6b8cc01b086dc5, M = {76} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:41:08 · history