Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 3deaeb6f8059…

magma 3deaeb6f8059
Size
381
Isomorphism class hash
3deaeb6f8059a0eef072c102eabb16b87658e679dc0c29709127054361f5d4ac
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 23:18:16
Display reorder
380,235,230,225,246,296,241,121,126,131,135,140,145,328,329,327,325,326,324,186,191,181,200,205,195,170,175,165,156,161,151,9,10,221,32,281,31,261,266,256,275,286,270,5,20,6,7,211,8,102,290,97,111,115,109,76,81,70,90,250,85,25,215,24,22,23,21,340,360,350,330,365,346,356,336,375,370,236,232,227,245,295,240,120,125,130,136,141,146,316,317,315,313,314,312,185,190,180,201,206,196,171,176,166,155,160,150,27,28,222,30,280,29,260,265,255,276,285,271,16,17,15,19,210,18,100,291,95,110,116,105,75,80,71,91,251,86,14,216,26,11,12,13,341,361,351,331,366,345,355,335,376,371,237,233,228,247,297,242,122,127,132,137,142,147,302,301,300,305,303,304,187,192,182,202,207,197,172,177,167,157,162,152,41,42,223,44,282,43,262,267,257,277,287,272,0,35,2,34,212,33,101,293,96,113,118,107,77,82,72,92,252,87,40,217,39,37,38,36,342,362,352,332,367,347,357,337,377,372,238,234,229,248,298,243,123,128,133,138,143,148,318,319,320,321,322,323,188,193,183,203,208,198,173,178,168,158,163,153,55,56,224,58,283,57,263,268,258,278,288,273,46,47,45,49,213,48,103,292,98,112,117,106,78,83,73,93,253,88,53,218,54,50,51,52,343,363,354,333,368,348,358,338,378,373,239,231,226,249,299,244,124,129,134,139,144,149,309,310,311,306,307,308,189,194,184,204,209,199,174,179,169,159,164,154,1,69,220,68,284,67,264,269,259,279,289,274,4,61,3,60,214,59,104,294,99,114,119,108,79,84,74,94,254,89,66,219,65,63,64,62,344,364,353,334,369,349,359,339,379,374 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 = {72} 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 23:18:16 · history