Equation 677 Database

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Magma e66f2b1f225b…

magma e66f2b1f225b
Size
381
Isomorphism class hash
e66f2b1f225b0bf1ce757b06ca2256dae8bcdb42f0d6d614f716add27b8de452
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 23:38:22
Display reorder
380,110,46,9,39,326,78,2,77,117,281,112,42,11,41,328,80,240,4,73,119,113,43,6,36,329,81,250,5,74,114,108,44,7,37,324,82,260,1,75,115,241,251,262,270,282,111,47,10,40,327,79,291,3,72,118,109,45,8,38,325,83,271,0,76,116,292,330,375,343,348,349,337,342,331,336,374,181,212,221,205,304,193,222,200,188,288,183,214,217,207,301,195,248,224,202,190,184,215,218,208,300,196,258,225,203,191,185,210,219,209,302,197,268,226,198,186,249,259,269,278,289,182,213,216,206,305,194,298,223,201,189,180,211,220,204,303,192,277,227,199,187,299,367,378,362,360,361,365,363,366,364,377,61,147,103,154,310,22,96,15,68,280,63,149,105,150,306,18,244,98,17,70,64,144,106,151,307,19,255,99,12,71,65,145,107,152,308,20,265,100,13,66,247,257,267,276,287,62,148,104,155,311,23,290,97,16,69,60,146,102,153,309,21,274,101,14,67,297,346,370,333,340,341,354,332,347,355,371,27,170,50,177,319,140,57,133,34,286,29,172,52,179,321,142,246,59,135,30,24,173,53,174,322,143,256,54,136,31,25,168,48,175,323,138,266,55,137,32,245,254,264,273,283,28,171,51,178,320,141,296,58,134,35,26,169,49,176,318,139,275,56,132,33,293,339,379,353,334,335,358,352,338,359,372,122,228,157,235,314,93,164,86,129,284,124,230,159,237,316,95,242,166,88,131,125,231,160,238,317,90,252,167,89,126,120,232,161,239,312,91,261,162,84,127,243,253,263,272,285,123,229,158,236,315,94,294,165,87,130,121,233,156,234,313,92,279,163,85,128,295,357,376,345,350,351,368,344,356,369,373 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#a5dba37ae82f5d1e2c854105d6ba510f1387eb5ee3dcc59dd48a683e84cf35f4, M = {66} 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 23:38:23 · history