Equation 677 Database

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Magma 16a5b9a9cab9…

magma 16a5b9a9cab9
Size
321
Isomorphism class hash
16a5b9a9cab9c822bc8f0275b79af486e4bed427437eb76b512c4e6685211673
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 22:33:18
Display reorder
311,248,244,275,269,66,174,41,223,67,173,40,222,171,69,42,220,172,68,43,221,268,249,245,274,216,167,45,63,217,168,46,64,215,166,44,65,170,219,48,62,267,273,246,247,169,218,47,61,186,187,185,189,190,188,191,192,288,289,290,287,300,302,309,317,286,279,284,281,183,133,114,165,184,134,115,164,135,181,118,161,136,182,116,162,137,180,117,163,157,132,112,176,283,280,278,285,156,131,113,175,128,159,111,179,129,160,109,177,130,158,110,178,207,208,206,203,204,205,213,214,211,209,210,212,310,306,303,318,14,77,119,36,15,37,78,120,235,242,252,259,38,16,75,121,243,236,251,260,39,17,76,122,123,34,71,18,124,35,72,19,125,33,70,20,241,261,250,237,31,126,74,21,32,127,73,22,10,8,9,13,11,12,201,202,294,292,293,295,307,319,308,315,282,277,291,276,153,1,29,194,152,0,30,193,232,266,240,270,2,155,28,196,3,154,27,195,198,4,24,151,271,233,238,265,197,5,23,150,6,199,26,148,7,200,25,149,234,272,239,264,54,52,53,50,51,49,60,58,55,56,57,59,304,305,301,316,147,83,104,96,145,97,84,105,146,98,82,103,95,143,79,107,93,144,80,108,94,142,81,106,258,255,253,263,257,256,254,262,102,89,88,138,90,100,85,141,91,101,86,139,92,99,87,140,224,225,226,227,228,229,230,231,298,296,297,299,313,312,314,320 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#5e80e1c2dc82944cee69cb7089d21c45f5ab65bc382c5d130a060fbb3f31d2ae, 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 22:33:19 · history