Equation 677 Database

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Magma 2728e9a7b085…

magma 2728e9a7b085
Size
321
Isomorphism class hash
2728e9a7b0850d84c4825760182e1163b5a570943d8074f3087dfa4332cb1738
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 22:55:00
Display reorder
300,157,229,75,135,155,158,230,136,76,153,156,228,77,137,154,232,160,74,134,151,233,161,72,132,152,231,159,73,133,150,235,163,81,141,146,236,164,82,142,144,234,162,83,143,145,166,238,80,140,149,167,239,78,138,147,165,237,79,139,148,305,308,312,315,258,257,243,259,256,261,260,262,244,263,253,252,245,254,255,269,268,242,270,271,273,272,240,274,275,265,264,241,266,267,280,281,249,282,283,284,285,250,286,287,277,276,251,278,279,292,293,248,294,295,297,296,246,298,299,288,289,247,290,291,319,320,317,318,36,66,8,18,31,37,67,19,6,32,38,68,7,20,30,69,39,11,21,34,70,40,9,22,35,71,41,10,23,33,64,42,3,16,29,65,43,4,17,27,63,44,5,15,28,45,60,2,12,25,46,61,1,13,26,47,62,0,14,24,302,316,313,301,114,198,48,173,91,115,199,171,49,92,116,200,50,172,90,201,117,51,169,94,202,118,52,170,95,203,119,53,168,93,196,112,54,179,89,197,113,55,177,87,195,111,56,178,88,108,192,57,175,85,109,193,58,176,86,110,194,59,174,84,310,303,311,304,217,181,120,98,211,218,182,96,121,212,216,180,122,97,210,184,220,123,101,214,185,221,124,99,215,183,219,125,100,213,187,223,126,104,209,188,224,127,102,207,186,222,128,103,208,226,190,129,107,205,227,191,130,105,206,225,189,131,106,204,309,307,314,306 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#c6a869941d5f836cd5f826f4a41a523fb37d651c2417bcc51f4579b275cefef3, 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 22:55:01 · history