Equation 677 Database

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Magma 51b7f8fb2c0c…

magma 51b7f8fb2c0c
Size
321
Isomorphism class hash
51b7f8fb2c0c4fb7ab5895832fa5b8deee106472712110a58d905805ea295c57
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 22:37:01
Display reorder
300,249,4,250,68,233,215,5,66,231,97,3,244,246,67,232,54,214,1,64,229,212,55,0,65,230,213,56,2,63,228,10,49,59,219,224,11,50,57,220,222,9,48,58,221,223,52,6,62,218,227,53,7,60,216,225,217,51,8,61,226,316,314,311,304,299,70,297,296,298,288,71,289,290,291,69,295,292,293,294,283,281,73,280,282,285,287,74,284,286,276,279,72,277,278,76,263,261,260,262,77,255,253,252,254,75,259,257,256,258,275,79,273,272,274,267,80,264,265,266,269,271,78,268,270,317,319,320,318,92,37,167,162,186,168,38,163,187,90,36,91,169,161,185,88,166,40,158,182,164,89,41,159,183,165,87,39,160,184,43,83,153,173,177,44,81,154,174,178,42,82,152,175,176,86,46,156,172,180,84,47,157,170,181,171,85,45,155,179,301,302,307,308,248,141,35,115,251,33,142,113,243,93,140,245,34,114,247,96,31,144,111,242,32,94,145,112,240,30,95,143,110,241,147,101,106,26,234,148,102,104,24,235,146,103,105,25,236,100,150,109,29,237,98,151,107,27,238,28,99,149,108,239,315,303,313,305,119,17,191,139,211,192,15,137,209,120,16,121,193,138,210,118,190,13,135,207,188,116,14,136,208,189,117,12,134,206,23,125,130,197,202,21,126,128,198,200,22,127,129,199,201,124,19,133,196,205,122,20,131,194,203,195,123,18,132,204,309,312,310,306 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#65ec2d14586b016399098bfd783683584e63e97f4655962a7b7e32e1fef46a76, 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 22:37:02 · history