Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 7fb3d2320c69…

magma 7fb3d2320c69
Size
381
Isomorphism class hash
7fb3d2320c698d32d9dcf1bf6c418640b68d6678309ef7c7a517c6cb0cbc0c7c
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 23:41:40
Display reorder
380,251,241,261,271,281,291,31,32,33,34,35,30,46,47,42,43,44,45,222,231,180,190,201,212,115,116,117,118,119,114,39,40,41,36,37,38,278,288,298,248,258,268,28,29,24,25,26,27,209,218,228,236,186,196,315,316,313,314,312,329,111,113,108,110,109,112,370,365,338,332,351,341,378,368,340,339,250,240,260,270,280,290,56,57,58,59,54,55,3,4,5,1,0,2,220,238,189,199,208,210,148,149,144,145,146,147,11,6,7,8,9,10,274,284,294,244,254,264,48,49,50,51,52,53,203,214,224,233,183,193,317,318,319,320,321,322,154,150,151,153,152,155,372,367,330,355,331,333,374,360,334,342,259,249,269,279,289,299,17,12,13,14,15,16,166,167,162,163,164,165,229,237,187,197,207,219,124,125,120,121,122,123,159,160,161,156,157,158,275,285,295,245,255,265,23,18,19,20,21,22,204,215,225,234,184,194,304,305,301,300,302,303,130,126,127,129,128,131,379,363,336,353,352,357,375,366,356,335,252,242,262,272,282,292,95,90,91,92,93,94,135,136,137,132,133,134,221,230,181,191,200,211,77,72,73,74,75,76,138,139,140,141,142,143,276,286,296,246,256,266,85,86,87,88,89,84,205,216,226,239,188,198,311,306,307,308,309,310,79,81,82,78,83,80,371,364,348,346,337,345,376,361,354,347,257,247,267,277,287,297,69,70,71,66,67,68,168,169,170,171,172,173,227,235,185,195,206,217,102,103,104,105,106,107,176,177,178,179,174,175,273,283,293,243,253,263,63,64,65,60,61,62,202,213,223,232,182,192,326,327,328,323,324,325,100,96,97,99,98,101,377,362,343,349,350,358,373,369,359,344 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#b66edbbdcc18ab822aeb8c0e517cc0500614bfcd68d760a94b6b8cc01b086dc5, M = {73} 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 23:41:41 · history