Equation 677 Database

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Magma 1b99879a3d30…

magma 1b99879a3d30
Size
381
Isomorphism class hash
1b99879a3d301d11dd36a4c6b37cf4a29ae567f30d997cc83e3ffcc6c7b3effa
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:49:22
Display reorder
380,163,173,168,158,298,153,327,328,329,324,325,326,113,103,108,123,118,288,8,13,3,23,268,17,48,273,43,33,38,28,59,64,54,74,279,69,89,94,99,79,84,284,198,203,193,183,188,178,228,233,223,213,218,208,253,263,258,248,238,243,128,138,133,293,143,148,343,333,358,362,338,354,349,373,377,368,160,171,166,155,296,150,305,303,304,302,301,300,112,102,107,122,117,287,5,10,0,21,265,16,45,271,40,31,36,25,56,61,51,70,276,66,86,90,95,75,80,281,195,200,190,180,185,176,225,231,220,211,216,206,251,261,256,245,235,240,127,137,132,292,142,147,341,331,357,360,335,351,345,371,379,366,162,172,167,157,297,152,320,318,319,323,321,322,111,100,106,120,115,286,6,11,1,20,266,19,46,270,41,30,35,26,58,63,53,73,278,68,88,93,98,78,83,283,197,201,192,182,187,177,226,230,221,210,215,205,250,260,255,246,236,241,126,135,130,291,140,145,340,330,356,361,336,353,348,370,375,367,161,170,165,156,295,151,308,306,307,311,309,310,110,101,105,121,116,285,7,12,2,22,267,15,47,272,42,32,37,27,57,62,52,72,277,67,87,92,97,77,82,282,196,202,191,181,186,175,227,232,222,212,217,207,252,262,257,247,237,242,125,136,131,290,141,146,342,332,355,363,337,352,347,372,376,365,164,174,169,159,299,154,315,316,317,312,313,314,114,104,109,124,119,289,9,14,4,24,269,18,49,274,44,34,39,29,55,60,50,71,275,65,85,91,96,76,81,280,199,204,194,184,189,179,229,234,224,214,219,209,254,264,259,249,239,244,129,139,134,294,144,149,344,334,359,364,339,350,346,374,378,369 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#edf00a573dad398077d9e9a7f74ac5f2ae5601c41b127cdfd29539dca9f6b98a, M = {76} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:49:23 · history