Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma fae1077e4919…

magma fae1077e4919
Size
381
Isomorphism class hash
fae1077e4919a5faa5c1e6a1b6e25786e544e973ba020c178cc67172acf3b288
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 23:42:41
Display reorder
380,270,13,12,4,211,5,286,230,235,226,215,220,41,295,36,26,30,21,115,106,111,101,290,96,160,153,158,176,166,171,66,56,61,50,241,45,146,136,141,130,121,126,323,321,322,320,318,319,246,251,255,261,266,276,76,70,82,85,90,281,190,185,180,200,205,196,350,330,355,365,341,336,345,371,361,376,273,17,16,0,213,1,288,233,238,228,218,223,43,298,38,28,33,23,119,109,114,104,294,99,163,152,157,178,168,173,67,57,62,52,242,47,148,138,143,133,124,129,308,306,307,311,309,310,247,252,257,260,265,275,77,71,84,86,91,280,193,188,183,203,208,198,354,333,358,366,340,338,348,373,363,377,274,19,18,3,214,2,289,234,239,229,219,224,44,299,39,29,34,24,116,105,110,100,291,95,164,151,156,179,169,174,69,59,64,54,244,49,149,139,144,134,120,125,313,314,312,316,317,315,249,254,259,264,269,279,79,74,83,89,94,284,194,189,184,204,209,199,351,334,359,368,344,339,349,374,364,379,271,8,9,11,210,10,285,231,236,225,216,221,40,296,35,25,31,20,117,107,112,102,292,97,161,154,159,175,165,170,65,55,60,51,240,46,145,135,140,131,122,127,327,328,329,324,325,326,245,250,256,263,268,278,75,73,81,88,93,283,191,186,181,201,206,195,352,331,356,369,343,335,346,370,360,375,272,15,14,7,212,6,287,232,237,227,217,222,42,297,37,27,32,22,118,108,113,103,293,98,162,150,155,177,167,172,68,58,63,53,243,48,147,137,142,132,123,128,303,304,305,301,300,302,248,253,258,262,267,277,78,72,80,87,92,282,192,187,182,202,207,197,353,332,357,367,342,337,347,372,362,378 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#c3f553b30d54716d9e2e87cb9ed350bbbf2e522a2867abba1f7ef649b9b0800a, M = {67} 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 23:42:42 · history