Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma d72934cbab53…

magma d72934cbab53
Size
381
Isomorphism class hash
d72934cbab537adf6e2d050fab7e02840fee9bf1cdb6797259dd67fabbd303af
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 23:45:54
Display reorder
380,16,15,17,12,13,14,6,7,8,9,10,11,3,4,5,1,0,2,28,29,24,25,26,27,200,205,181,185,190,195,286,291,295,271,276,281,18,19,20,21,22,23,246,251,256,260,265,241,226,230,235,211,216,221,321,322,323,318,319,320,150,171,156,161,166,176,330,348,361,367,357,350,371,331,338,376,54,53,55,56,57,58,49,50,51,52,118,48,46,47,42,43,44,45,38,39,40,41,36,37,204,209,183,189,194,199,288,294,299,273,278,283,33,34,35,30,31,32,249,254,259,264,269,243,229,234,239,213,219,224,324,325,326,327,328,329,153,174,158,163,169,179,341,347,363,366,355,353,373,337,342,378,68,67,69,70,65,66,63,64,59,60,61,62,85,86,87,88,83,84,80,81,82,77,78,79,201,206,180,186,191,196,285,290,296,270,275,280,72,73,74,75,76,71,245,250,255,261,266,240,225,231,236,210,215,220,312,313,314,315,316,317,151,170,155,160,165,175,340,345,362,368,358,351,370,336,333,375,102,105,103,104,101,119,99,100,95,96,97,98,90,91,92,93,94,89,112,113,114,115,116,117,203,208,184,188,193,198,289,293,298,274,279,284,111,106,107,108,109,110,248,253,258,263,268,244,228,233,238,214,218,223,302,303,304,305,301,300,154,173,159,164,168,178,339,346,364,369,359,352,374,332,343,379,145,144,146,147,148,149,139,140,141,142,143,138,136,137,132,133,134,135,128,129,130,131,126,127,202,207,182,187,192,197,287,292,297,272,277,282,123,124,125,120,121,122,247,252,257,262,267,242,227,232,237,212,217,222,306,307,308,309,310,311,152,172,157,162,167,177,335,349,360,365,356,354,372,334,344,377 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#dc50bff4268d4e886a12bccb100fd4b53117610e2c07e48d4c792db14c6c3b47, 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 23:45:55 · history