Equation 677 Database

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Magma 32a16967dd20…

magma 32a16967dd20
Size
321
Isomorphism class hash
32a16967dd204509c3fc31911339b8c5beaf157d24b4e00bca2e43a3f08e6a20
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 22:45:38
Display reorder
300,52,47,186,187,32,45,53,30,188,189,31,51,46,191,190,48,43,35,185,184,49,44,33,181,180,50,42,34,183,182,58,38,27,198,199,59,36,28,201,200,57,37,29,203,202,41,54,26,197,196,192,39,55,24,193,40,56,25,195,194,315,316,306,305,162,265,267,266,264,269,163,268,271,270,273,164,272,275,274,165,260,261,263,262,166,252,253,255,254,167,256,257,259,258,160,289,288,290,291,161,293,292,294,295,159,296,297,298,299,284,156,285,286,287,278,277,157,276,279,281,158,280,282,283,320,319,317,318,65,234,217,216,235,237,63,236,219,218,238,64,239,221,220,61,233,232,223,222,62,229,228,225,224,60,231,230,227,226,71,246,247,212,213,69,248,249,214,215,70,250,251,211,210,244,67,245,204,205,206,240,68,241,207,242,66,243,208,209,309,310,307,308,18,90,146,171,7,91,19,8,144,172,6,20,92,145,173,21,93,10,149,170,22,94,11,147,168,23,95,9,148,169,16,88,5,152,177,17,89,3,150,178,15,87,4,151,179,84,12,0,155,176,153,85,13,2,174,86,14,1,154,175,311,312,304,301,78,98,109,135,131,96,79,129,110,136,130,80,97,108,137,81,101,127,112,134,82,99,128,113,132,83,100,126,111,133,76,104,122,115,141,77,102,120,116,142,75,103,121,114,143,107,72,125,118,140,119,105,73,123,138,106,74,124,117,139,313,314,302,303 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#96b025dbf47c4a59dfaaf1b34262061bd74b6a84a8a9978c39bcd4e78b704a7c, 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 22:45:39 · history