Equation 677 Database

← all  ·  ← by size  ·  ← size 321

Magma 3be0813bca30…

magma 3be0813bca30
Size
321
Isomorphism class hash
3be0813bca300d06b2059e155fea74c79579a059629935cd7501a2a782f001ea
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:50:27
Display reorder
300,284,283,282,286,287,285,281,279,280,277,278,276,177,178,179,176,174,175,168,169,170,171,172,173,74,72,73,77,75,76,80,78,79,83,81,82,165,166,167,164,162,163,156,157,158,159,160,161,234,235,236,237,238,239,232,233,231,228,229,230,303,305,311,316,125,124,123,120,121,122,130,131,129,126,127,128,91,92,90,94,95,93,89,87,88,85,86,84,104,102,103,107,105,106,99,100,101,98,96,97,115,116,114,118,119,117,113,111,112,109,110,108,142,143,141,138,139,140,133,134,132,136,137,135,313,318,319,320,57,59,58,55,56,54,50,48,49,53,51,52,41,39,40,37,38,36,47,45,46,43,44,42,246,247,248,249,250,251,244,245,243,240,241,242,188,186,187,191,189,190,183,184,185,182,180,181,290,288,289,293,291,292,296,294,295,299,297,298,302,308,312,317,257,256,255,252,253,254,262,263,261,258,259,260,19,20,18,22,23,21,17,15,16,13,14,12,30,31,32,33,34,35,28,29,27,24,25,26,199,200,198,202,203,201,197,195,196,193,194,192,151,152,150,154,155,153,149,147,148,145,146,144,304,306,309,315,65,64,63,60,61,62,70,71,69,66,67,68,267,268,269,266,264,265,273,274,275,272,270,271,10,11,9,6,7,8,0,2,1,4,5,3,220,221,219,216,217,218,226,227,225,222,223,224,212,210,211,215,213,214,207,208,209,206,204,205,301,307,310,314 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {61} 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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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 2026-10-01 22:50:28 · history