Equation 677 Database

← all  ·  ← by size  ·  ← size 399

Magma d6e2c51b949c…

magma d6e2c51b949c
Size
399
Isomorphism class hash
d6e2c51b949c7ac1e63b096595c7c6ba4da0dd758fe71ea56a62eaecf2c88512
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 10:48:19
Display reorder
16,17,9,10,11,12,13,14,15,1,0,2,3,4,5,6,7,8,398,135,101,112,113,136,102,114,137,103,115,138,104,116,139,105,108,140,106,109,141,107,110,142,99,143,111,100,128,121,94,129,122,95,130,123,96,131,124,97,132,125,98,133,117,90,134,118,91,126,119,92,127,120,93,146,147,148,149,150,151,152,144,145,155,156,157,159,160,161,153,154,158,389,383,385,397,296,253,283,284,288,254,285,289,255,286,290,256,287,291,257,279,292,258,280,293,259,281,294,260,295,282,252,305,276,262,297,277,263,298,278,264,299,270,265,300,271,266,301,272,267,302,273,268,303,274,269,304,275,261,234,235,236,237,238,239,240,241,242,243,244,245,247,248,249,250,251,246,384,396,395,382,232,192,208,209,233,193,210,225,194,211,226,195,212,227,196,213,228,197,214,229,189,215,230,190,231,207,191,216,201,185,217,202,186,218,203,187,219,204,188,220,205,180,221,206,181,222,198,182,223,199,183,224,200,184,169,170,162,163,164,165,166,167,168,178,179,171,173,174,175,176,177,172,388,390,387,386,348,321,329,330,349,322,331,350,323,332,342,315,324,343,316,325,344,317,326,345,318,327,346,319,347,328,320,357,338,314,358,339,306,359,340,307,351,341,308,352,333,309,353,334,310,354,335,311,355,336,312,356,337,313,374,375,376,377,369,370,371,372,373,367,368,360,362,363,364,365,366,361,392,391,393,394,42,82,29,30,43,83,31,44,84,32,36,85,33,37,86,34,38,87,35,39,88,27,40,89,41,28,81,51,22,75,52,23,76,53,24,77,45,25,78,46,26,79,47,18,80,48,19,72,49,20,73,50,21,74,67,68,69,70,71,63,64,65,66,60,61,62,55,56,57,58,59,54,379,378,380,381 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 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#b97e7cb00def8c6c5bb50216e42de989c133f1146dae1ca56e834f171e366e99, M = the submagma generated by {0} (19 elements) 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: 21.

last edited by qawbecrdtey at 2026-10-06 10:48:20 · history