Equation 677 Database

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Magma cc712e94357b…

magma cc712e94357b
Size
321
Isomorphism class hash
cc712e94357b11270c287e6855b0e2bfd538b7b6a92ba3e612130992ae7fe614
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 22:27:47
Display reorder
300,164,41,63,137,184,185,42,165,61,138,43,183,163,62,136,186,166,121,208,214,167,187,122,64,244,248,233,227,65,139,162,44,68,182,135,160,45,66,180,133,161,46,67,181,134,47,159,70,178,131,207,216,69,179,132,48,247,240,232,228,313,310,308,315,281,283,196,280,282,286,287,285,197,284,279,278,276,198,277,294,292,295,199,293,297,298,299,200,296,288,290,291,201,289,273,275,194,274,272,264,267,195,266,265,268,271,193,270,269,259,256,190,258,257,263,260,191,262,261,255,252,192,254,253,320,319,318,317,96,25,56,71,226,225,236,243,57,72,24,116,95,55,209,213,98,21,59,73,99,115,22,60,74,97,114,23,58,75,94,16,54,112,76,92,17,52,110,77,93,15,53,111,78,19,90,50,212,210,20,91,51,113,79,18,242,239,224,219,305,316,302,301,173,145,30,126,154,155,146,174,31,127,144,153,172,29,125,157,176,148,26,129,177,158,149,27,130,175,156,147,28,128,171,143,14,215,189,217,141,204,151,218,170,142,13,152,188,140,169,11,246,234,245,231,237,230,249,229,168,12,150,124,314,309,311,312,8,85,33,117,105,106,86,9,34,118,84,104,10,32,119,108,7,88,36,120,5,109,89,37,123,6,107,87,35,83,2,202,38,103,81,3,203,39,101,80,0,235,205,102,211,49,1,206,222,241,251,220,238,223,221,250,4,40,100,82,303,307,304,306 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#3a1e3dea02005faeb7a32ea89e0ebcd7060d0e295c5a20add7fb441719113d75, M = {60} 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 22:27:47 · history