Equation 677 Database

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Magma 1cd382c31afc…

magma 1cd382c31afc
Size
321
Isomorphism class hash
1cd382c31afce8f149116b07afa7026a8add9be1113a71b64a17f5155ef217a4
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 22:28:29
Display reorder
300,38,83,122,9,210,36,10,81,120,211,37,11,82,121,212,41,79,8,125,213,39,80,6,123,214,40,78,7,124,215,128,74,44,1,208,126,72,42,0,209,127,73,43,2,207,77,131,47,3,204,75,129,45,4,205,76,130,46,5,206,311,312,305,302,244,291,290,288,289,245,292,294,295,293,243,296,298,299,297,240,287,284,286,285,241,279,276,278,277,242,282,280,283,281,254,255,250,252,253,259,258,251,256,257,262,263,249,260,261,267,266,246,265,264,271,270,247,269,268,274,275,248,273,272,317,320,319,318,139,23,225,90,237,140,91,21,226,238,138,92,22,227,239,142,19,93,224,236,143,20,94,222,234,141,18,95,223,235,216,14,137,88,228,217,12,135,89,229,218,13,136,87,230,17,219,133,84,231,15,220,134,85,232,16,221,132,86,233,316,309,308,313,104,184,175,201,153,102,202,185,176,154,103,203,183,174,155,107,180,200,178,152,105,181,198,179,150,106,182,199,177,151,173,190,99,192,144,171,191,100,193,145,172,189,101,194,146,186,169,98,195,147,187,170,96,196,148,188,168,97,197,149,314,306,304,301,24,61,49,159,108,25,160,62,50,109,26,161,60,48,110,27,64,158,52,111,28,65,156,53,112,29,63,157,51,113,55,67,30,165,114,56,68,31,166,115,54,66,32,167,116,70,58,33,164,117,71,59,34,162,118,69,57,35,163,119,315,303,307,310 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#458b3cfe489c9903ffdf95802569f7fced83cfa9f913419e94bc2fd3ec4c05bf, 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 22:28:30 · history