Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma c0a94ca119e7…

magma c0a94ca119e7
Size
381
Isomorphism class hash
c0a94ca119e74bd49425cdae48569a5b0cf4efac0bf0945460bca94a07fd5817
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 23:18:09
Display reorder
380,291,285,297,272,277,281,112,119,106,126,131,121,11,12,13,8,9,10,97,98,228,94,95,96,83,81,82,238,7,6,304,305,303,300,302,301,170,175,165,186,191,181,156,161,151,140,145,135,233,80,79,77,78,76,248,253,243,263,267,258,196,201,206,210,215,220,330,348,343,338,361,353,355,375,368,371,294,286,295,271,276,280,113,117,108,128,133,123,29,30,28,32,33,31,18,17,226,16,14,15,25,23,24,236,26,27,323,321,322,320,318,319,173,178,168,188,193,183,158,163,153,143,148,138,231,22,21,75,20,19,246,251,241,260,266,255,198,203,208,213,218,223,333,346,341,336,363,350,356,378,367,373,290,287,296,270,275,282,111,116,105,125,130,120,0,2,1,4,5,3,92,93,227,89,90,91,62,63,64,237,60,61,329,327,328,326,324,325,171,176,166,185,190,180,155,160,150,141,146,136,232,55,56,57,58,59,247,252,242,262,265,257,195,200,205,211,216,221,331,347,342,337,360,352,357,376,365,370,293,289,299,274,279,284,114,118,109,129,134,124,40,41,42,43,104,44,102,103,229,99,100,101,51,52,50,239,54,53,315,316,317,312,313,314,174,179,169,189,194,184,159,164,154,144,149,139,234,45,46,49,47,48,249,254,244,264,269,259,199,204,209,214,219,224,334,349,344,339,364,354,359,379,369,374,292,288,298,273,278,283,110,115,107,127,132,122,35,36,34,38,39,37,87,88,225,84,85,86,67,65,66,235,68,69,307,308,306,310,311,309,172,177,167,187,192,182,157,162,152,142,147,137,230,73,74,72,70,71,245,250,240,261,268,256,197,202,207,212,217,222,332,345,340,335,362,351,358,377,366,372 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#0c1c8b18119133fb8debdb5d149d6db1ac93e4c65e1bffaee2a0311d537b261b, M = {71} 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 23:18:10 · history