Equation 677 Database

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Magma 3469762dc1ff…

magma 3469762dc1ff
Size
321
Isomorphism class hash
3469762dc1ffa221233661c80ca7b551e2a086ffc8b473cf9655c2213fa2e5db
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 22:26:54
Display reorder
312,254,250,246,275,99,90,68,223,89,100,69,222,102,87,71,220,101,88,70,221,255,249,247,274,105,83,65,216,103,84,66,217,104,82,67,215,107,86,64,219,256,248,245,273,106,85,63,218,189,190,188,185,186,187,191,192,291,289,290,292,304,302,308,317,294,277,288,284,205,29,130,81,28,206,131,80,209,25,134,77,207,26,132,78,208,27,133,79,211,20,128,73,295,276,287,283,210,21,129,72,214,23,127,75,212,24,125,76,213,22,126,74,184,182,183,180,181,179,175,173,177,178,176,174,310,301,306,315,119,158,170,30,118,157,169,31,268,261,271,236,117,156,172,33,260,267,272,237,116,155,171,32,124,163,166,35,122,161,167,36,123,162,168,34,262,269,270,238,121,160,164,38,120,159,165,37,44,42,43,40,41,39,46,45,278,293,280,279,303,319,305,316,281,285,286,282,49,91,114,59,92,50,115,60,239,251,259,244,47,93,113,61,48,94,112,62,53,95,109,58,241,252,257,243,54,96,108,57,52,97,111,55,51,98,110,56,240,253,258,242,195,193,194,198,196,197,201,199,203,204,202,200,307,309,300,318,4,143,148,14,5,144,149,15,142,3,150,16,1,139,147,17,0,140,145,18,2,141,146,19,233,263,265,234,232,264,266,235,9,135,154,13,6,137,153,10,7,138,151,11,8,136,152,12,224,225,226,227,228,229,230,231,298,296,297,299,314,313,311,320 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#3180ad8dfd10ba7152583c35a71774bceecf2852df6e850dd8c0dada693f6036, 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 22:26:55 · history