Equation 677 Database

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Magma 2403aab9b5f3…

magma 2403aab9b5f3
Size
321
Isomorphism class hash
2403aab9b5f3bf32b3e59a92e0e3a9bbf0a491094732cb4bcb160e9292d63bc7
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 22:55:35
Display reorder
300,91,119,123,239,243,92,124,237,244,117,90,118,125,238,245,122,94,115,235,242,95,120,116,236,240,93,121,114,234,241,89,129,110,230,249,228,87,130,108,250,88,131,109,229,251,128,85,113,233,248,126,86,111,231,246,127,84,112,232,247,315,311,303,304,57,265,264,267,266,58,268,271,270,269,59,272,273,275,274,260,56,261,263,262,54,252,253,255,254,55,256,257,259,258,48,288,289,290,291,294,49,293,292,295,50,297,296,298,299,285,51,284,287,286,276,52,277,279,278,281,53,280,283,282,319,317,320,318,14,82,225,98,68,12,226,96,66,83,13,81,227,97,67,224,17,78,101,71,15,222,79,99,69,16,223,80,100,70,20,216,73,104,63,102,18,217,74,64,19,218,72,103,65,219,23,76,107,62,220,21,77,105,60,221,22,75,106,61,302,314,316,301,42,207,2,186,203,43,1,187,201,208,44,209,0,188,202,5,45,206,189,199,46,3,204,190,200,47,4,205,191,198,40,8,213,184,194,185,41,6,214,192,39,7,215,183,193,11,36,212,180,197,9,37,210,181,195,10,38,211,182,196,307,313,308,310,33,147,163,171,139,34,164,172,140,148,35,149,162,173,138,166,32,146,170,142,30,167,144,168,143,31,165,145,169,141,24,161,153,177,137,178,25,159,154,135,26,160,155,179,136,157,27,152,176,133,158,28,150,174,134,156,29,151,175,132,309,312,305,306 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#cd941b7de786c28317b7a103413c14ee77b5f1d3c398e3760811607e92439ad2, 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 22:55:36 · history