Equation 677 Database

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Magma d4f1adcf3d97…

magma d4f1adcf3d97
Size
321
Isomorphism class hash
d4f1adcf3d97b04b400d0209bb93e87b8a137fb0a2ea699f22b85508a45804c6
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 22:21:18
Display reorder
300,139,10,79,88,100,140,11,77,89,98,138,9,78,90,99,141,8,75,87,97,0,142,76,85,227,220,233,224,86,96,137,3,72,80,93,135,4,70,81,91,136,1,71,82,92,6,133,74,83,95,7,134,73,84,94,5,232,223,225,226,303,305,309,307,280,42,281,283,282,284,40,285,287,286,277,41,276,279,278,292,38,293,295,294,39,296,297,299,298,37,289,288,291,290,272,48,273,274,275,265,46,264,266,267,269,47,268,270,271,44,256,257,258,259,45,260,261,262,263,43,252,253,254,255,317,319,318,320,155,13,156,55,229,236,221,237,56,107,153,12,154,54,106,159,16,160,58,109,14,161,162,59,110,15,157,158,57,108,152,19,151,53,105,148,17,147,51,103,150,18,149,52,104,22,144,143,49,101,20,146,145,50,102,21,235,234,222,228,304,306,316,315,165,66,182,195,191,163,194,183,188,28,164,65,184,189,2,168,68,181,186,30,69,166,179,187,31,67,167,180,185,29,171,212,174,219,214,169,218,175,207,203,170,206,176,213,208,200,173,177,251,247,250,238,239,245,241,244,172,178,201,197,301,308,302,310,117,60,128,192,190,118,193,129,32,26,116,61,127,33,27,120,62,131,36,24,63,121,132,34,25,64,119,130,35,23,115,211,126,216,215,113,217,124,204,202,114,205,125,210,209,199,112,123,248,246,249,230,231,242,240,243,111,122,198,196,313,311,314,312 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#0c204955552ad126415d2d3170da1bc3e83549814dfd47378340ca39d32aede4, 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 22:21:19 · history