Equation 677 Database

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Magma 1ef9a8dc0d68…

magma 1ef9a8dc0d68
Size
321
Isomorphism class hash
1ef9a8dc0d68847a73d87c80dcaf4e054ae973d735026866c27f055a48c14f32
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 22:59:18
Display reorder
311,236,275,267,233,21,179,15,223,20,222,180,14,181,18,220,16,182,19,221,17,268,235,274,234,183,25,13,216,184,26,11,217,185,24,12,215,22,186,9,219,237,269,232,273,23,187,10,218,142,143,141,145,146,144,147,148,286,287,288,285,307,300,309,318,294,282,276,278,205,2,27,74,206,75,3,28,0,209,73,29,1,207,71,30,204,208,72,31,7,211,32,79,277,295,279,283,8,210,33,80,214,6,34,78,212,4,35,76,213,5,36,77,159,160,158,162,163,161,165,166,167,168,169,164,310,301,303,315,156,173,45,57,157,46,56,172,263,265,241,245,48,155,171,55,242,262,264,244,47,154,170,54,50,149,62,178,51,150,60,176,49,151,61,177,261,243,246,266,152,53,59,175,153,52,58,174,198,196,197,201,199,200,203,202,292,293,291,290,302,319,306,314,289,284,281,280,192,63,39,135,193,136,64,40,247,272,258,238,65,194,134,37,66,195,133,38,67,190,43,140,248,271,240,260,68,191,44,139,189,69,42,137,188,70,41,138,270,249,239,259,92,90,91,88,89,87,83,81,85,86,84,82,304,308,305,317,128,95,118,109,126,119,107,93,127,94,117,108,121,124,98,112,122,125,96,110,120,123,97,111,255,257,252,251,254,256,253,250,116,132,106,99,130,114,105,102,131,115,103,100,129,113,104,101,224,225,226,227,228,229,230,231,298,296,297,299,313,316,312,320 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#dc3952d3945a57ff89efbf9c91902a27e7bb606727f60175866197715516bbc5, 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 22:59:19 · history