Equation 677 Database

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Magma 420b620868e8…

magma 420b620868e8
Size
321
Isomorphism class hash
420b620868e8e2403b09bab7505bec8ff6700b4efe35c3d74716fc3a5307e329
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 22:38:00
Display reorder
300,99,41,15,240,241,100,39,16,242,243,101,40,17,244,245,37,98,14,246,247,96,38,12,248,249,36,97,13,250,251,21,105,47,237,236,22,106,45,239,238,23,107,46,234,235,104,20,43,229,228,102,18,44,231,230,103,19,42,233,232,314,313,303,305,265,58,264,266,267,268,59,269,270,271,272,57,273,274,275,54,260,261,262,263,252,55,253,254,255,56,256,257,258,259,289,288,49,291,290,292,293,50,295,294,296,297,48,299,298,285,284,52,286,287,277,276,53,278,279,281,280,51,282,283,319,318,317,320,171,114,31,159,183,172,115,32,160,184,173,116,30,161,185,117,170,34,158,182,168,118,35,156,180,119,169,33,157,181,29,177,112,165,189,27,178,113,166,190,28,179,111,167,191,176,25,108,164,188,174,26,109,162,186,175,24,110,163,187,307,311,302,301,83,70,87,143,128,81,71,88,141,126,82,69,89,142,127,66,79,86,139,131,80,67,84,140,129,68,78,85,138,130,93,74,61,134,123,94,72,62,132,124,95,73,60,133,125,77,92,64,137,122,75,90,65,135,120,76,91,63,136,121,308,315,312,316,147,0,196,216,206,148,2,197,217,204,149,1,195,218,205,4,146,192,219,209,144,5,193,220,207,3,145,194,221,208,202,153,7,222,212,203,154,8,223,210,201,155,6,224,211,152,198,10,225,215,150,199,11,226,213,151,200,9,227,214,304,309,310,306 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#7bddf6e5b82b5432712e2579d3d5db84306ca98ed650c79ff87e357573a5998e, 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 22:38:01 · history